Excellent question!

In general we can make several broad statements about the differences in how the war played out at sea in the two theaters.

1. In the Pacific we cans ay in December of 1941 the Axis and Allies were much more evenly matched then in September of 1939. While the Allies would eventually out produce by orders of magnitude, the IJN had been built up over several decades with the sole purpose to challenge the USN for dominance. While the KM was the result of a mad scramble for about a decade to try to build a fleet, first as a balanced conventional force, then one designed for commerce raiding, then back, and thus effective at neither and hampered by small numbers. Even accounting for the Italian Fleet the RN was capable of meeting them both with sufficient numbers to have a good chance of success anywhere even with her global demands for ships.

2. The simple scale of the Pacific had a huge impact on how it was waged. The North Sea and North Atlantic are comparatively small and cramped, fleets were going to fight at knife fight ranges, ships could afford less range and still be useful, aircraft could be based ashore and didn't need as long of range.

While in the Pacific long range patrol was an absolute must, ships could be expected, and were designed to fight at virtually the maximum possible ranges, and both sides planned a long war over a series of atolls and islands which could serve as safe havens.

This of course meant the carrier took on a whole new importance in the Pacific. While it was useful in the Atlantic to fight subs, augment shire based patrols, and support landings. In the Pacific they were sine qua non for any naval thrust that hoped for success.

When it comes to High Command we can also draw some differences. While in Europe command was largely a multinational coalition affair, in the Pacific (admittedly discounting the CBI theater with the massive Commonwealth presence) it was a 100% US run show.

The war was broadly divided between the Pacific Ocean Area led by Nimitz, and the SW Pacific led by MacArthur.

Japanese ships differed in a few important respects compared to those of other navies.

• Firepower emphasis - Japan more than any other country emphasized the importance of maximum firepower at the greatest possible ranges. As a result of their experiences in the Sino-Japanese and particularly the Russo-Japanese wars, the IJN emphasized the ability to engage at greater distances than their potential opponents. Compared to their equivalents, the Japanese Fubuki class destoyers were larger, faster, better protected, and better armed. This emphasis on superior firepower was only exacerbated by the terms of the Washington Naval Treaty, where Japan was left with a 3:5 ratio of capital ship tonnage compared to the United States and Great Britain. Their ship designers began to emphasize qualitative superiority. The Yamato class is a tremendous example of this obsession with qualitative superiority.

• Cruisers - Japanese cruisers were divided along somewhat different lines compared to other nations of the time. The Kuma, Nagara, and Sendai class are traditionally called light cruisers in the west, but in practice were used in more of a destoryer leader role, acting as larger flagships for destroyer squadrons. The larger A type cruiser of the Myoko, Takao, and later Mogami class fit in well with the western idea of a heavy cruiser, but retained their torpedo armament well after other navies removed torpedos from their heavy cruisers. These A type cruiser were also generally considered to be top heavy and unstable, particularly the Takao and Mogami class, as a result of trying to cram too many weapons on too small a ship. If you are interested, the Tomozuru and Fourth Fleet incidents exposed design flaws in a number of Japanese ships.

• Aircraft Carriers - There are two main characteristics that distinguished American, British, and Japanese aircraft carriers. British aircraft carriers were designed to operate in the stormy North Atlantic, and were designed with what are called enclosed hangars, they had a ring of compartments between the aircraft hangar and the hull of the ship to keep the weather out. British carriers were also given armored flight decks. They were expected to mostly operate within the range of land based aircraft, and therefore needed to be able to continue flight operations even after sustaining hits to the flight deck. American carriers, in contrast, were expected to operate in the sunny south pacific, with nice weather, and land airbases few and far between. American carriers had their armor deck at the hangar level, which means bomb hits could penetrate the flight deck, and detonate in the hangar. American carriers also had open hangars, literally so, in many cases they could roll back a large metal curtain to open the hangar sides. This had several advantages, as it allowed aircraft to be prepared and warmed up in the hangar, before being spotted, and provided a convenient exit for explosives that detonated in the hangar. Japanese carriers had unarmored flight decks and enclosed hangars, arguably the worst combination of the two. The hangars were not protected from air dropped bombs, and any explosions were contained within hangar, forcing them down in the ship. For the results of this, see the Battle of Midway.

• Convoys - The Japanese did not operate their merchant fleet in convoys the same way the Americans and British did. WWII was the first time Japan had significant oversees territory to protect, and significant resources to be gained from them. During their previous wars, the role of the Imperial Navy had been primarily defensive, engaging enemy fleets relatively close to home. Because the Imperial Navy did not, for the most part, participate in the First World War, they did not fully appreciate the logistics involved in convoy protection, and did not invest significant resources in anti-submarine warfare and commerce protection until it was far too late. The Imperial Navy of the Second World War was designed with the almost single minded purpose to defeat the US Pacific Fleet in a surface engagement, all other considerations were secondary.

The Pacific was almost entirely run by the United States Navy, with the British Royal Navy playing only a very subsidiary role, and was fought against the Imperial Japanese Navy which at least had a proper battlefleet. Usually there were enough ships at sea in each fleet to justify having an admiral command the fleet with a support staff; albeit the US Navy added the innovation of having a back-up command staff on shore at Pearl Harbor who would plan for the next operation (and generate false signals to distract the Japanese and make them think there were two major US Fleets - 3rd and 5th - which were actually the same formation)

The North Atlantic by contrast was run primarily by the Royal Navy - albeit there was an enormous influx of US and other Allied ships - and was fought primarily against the German Kriegsmarine which was primarily a commerce-raiding force. Convoys were usually just commanded by a commodore (for the military escorts) assisted by a senior merchant ship Captain; while the Wolfpacks were commanded by a senior U-boat Captain. Both relied extensively on their shore HQ for directions, unlike the Pacific where fleet admirals could mostly act on their own.

From a strategic perspective the Pacific for both sides was really about the gradual seizure of key ports and airfields across the many islands of the Pacific. These facilities would allow the basing of land-based airpower, which could then disrupt enemy battlefleets and merchant shipping and prevent further advances. The Japanese, early on, took many of these islands with little resistance; whereas the American campaign was primarily aimed at retaking them in the face of prepared Japanese defenses. Naval battles, when fought, were meant primarily to facilitate or prevent these naval invasions. Indeed, pretty much every Pacific battle - from Coral Sea to Okinawa - ultimately revolved around trying to land/prevent the landing of a ground invasion force.

From a tactical perspective the Pacific demonstrated the dominance of naval air power in engagements, thus requiring the development of carrier fleets that could bring sufficient aircraft to suppress land-based aircraft defending these island bases. That said early in the war aircraft carriers were a finite and precious commodity which is why so many surface battles were also fought; particularly around Guadalcanal (at one point in this campaign Enterprise was the sole US carrier left in the Pacific, leading to the crew putting up a legendary sign that said "Enterprise vs Japan"). That said, based on these tactical requirements most surface ships progressively became anti-aircraft vessels with larger and larger anti-aircraft suites to support and protect the carriers. This was in many ways to the detriment of the Japanese, as their pre-war fleet was configured with a grand surface battle in mind and they weren't really able to fully reconfigure their fleet to the carrier mindset before most of their carrier pilots were killed at Midway.

From a submariner's perspective, the Pacific War is still somewhat riddled with misconceptions. The Japanese are traditionally said to have disdained submarine attacks against US merchant ships - supposedly due to honorable samurai warrior mentality (that paradoxically you don't see anywhere else in the IJN) - but in reality it seems to be that their submarine force had real reliability and fuel issues and could not really engage in the long-ranged cruises needed to intercept US supply ships.

American submarines meanwhile were extremely successful, which is also traditionally attributed to Japanese convoy / ASW practice incompetence, but this is also something of a myth. The Japanese in fact had decent sonar and some radar, and were in many ways close to the Royal Navy's capabilities throughout the war. Moreover, the Japanese merchant ships were very modern, being mainly new, oil-fired ships capable of 10+ knot speed. The Japanese therefore (rightly) believed that their modern merchant ships could outrun most of the US pre-war submarines and convoys were unnecessary; as they had a shortage of escort ships and wanted to keep most of them protecting the battlefleet.

However by 1943 the American Gato-class submarine was becoming available in large numbers, which could outrun the Japanese merchant ships on the surface. More importantly they were equipped with radar, allowing them to "see" enemy ships beyond visual range and hunt them down while still surfaced by remaining within radar range but outside of visual range (the US submarines only submerged on the final attack approach). This was a capability the U-boats never enjoyed and would have been challenging even for the Royal Navy; which resulted in mounting Japanese losses and the eventual adoption of small convoys of around half a dozen ships apiece. The small size of these convoys - again often mistaken for bad convoy practice by observers of the Battle of the Atlantic - was a result of the escort shortage (often with just one or two destroyers per convoy), and the fact that most trips were shorter than the long transatlantic voyage from America to Britain. The small Japanese convoys could, in fact, usually hop from island to island before night fell and remain in relative safety of the harbor for the most part.

Convoys in the Atlantic by contrast were huge - often consisting of 30+ ships at least. It was actually a gargantuan effort to just organize all of the shipping into these massive convoys; and numerous support ships (e.g. specialized rescue ships) were commissioned to aid these convoys.

That said most of the Atlantic convoys were actually uneventful - something like 90% of convoys got through without being attacked at all - due to all of the code-breaking and detection efforts in Britain that steered convoys away from potential trouble spots. The convoys were slow - often travelling at less than 10 knots - but quite frankly the U-boats were often even slower especially when they were submerged.

The unlucky remainder would have been safe from attacks by individual U-boats, but the Kriegmarine had developed "wolf pack" tactics that concentrated a dozen or so U-boats against each individual convoy. This often overstretched the convoy's escorts - usually about just six ships in ideal conditions or one escort in really desperate ones - which allowed the submarines to attack the merchant ships largely unmolested.

However the Kriegsmarine, having no capability to capture islands and with little airpower supporting them, were steadily beaten by a combination of increased escorts and Allied air superiority. Aircraft were particularly deadly to U-boats, as the planes were able to spot U-boats from afar and destroy them before they could close unto the convoy; especially when the aircraft had been equipped with ground-search radar. By 1943 sufficient escorts had been built to create "hunter-killer" groups, which were essentially reserve formations that could be rushed to trouble spots as needed.

All of these elements came together in the convoy battle ONS-5, which was in many ways a watershed for the Royal Navy. Despite heavy convoy losses the U-boats themselves lost 7 boats, which was an unacceptable rate of attrition. Several further battles resulted in equally heavy U-boat losses for fewer and fewer merchant ships sunk, resulting in the ultimate suspension of the U-boat campaign in 1943.

From a tactical perspective the ships that fought in the Atlantic tended to be smaller escorts focused on anti-submarine warfare, with radar and sonar being the prime "weapon" to find the U-boat. Actual anti-submarine weapons were usually rather primitive and low-key, such as the depth charge from World War 1 and the "hedgehog" (which was essentially a grenade launcher that dropped small bombs that could sink a submarine). Most importantly however Atlantic escorts had to have good sea-keeping qualities, as there was really no safe harbor between America and Britain that could be easily reached by a crippled merchant ship or escort. Indeed, quite a large number of ships went down in the Atlantic due to bad weather or damage rather than direct enemy action. The Japanese by contrast could afford somewhat more fragile ships because they had the coast of China and Indochina to harbor in.

Edit: Clarifications