There were massive differences between how every nation designed their ships. Ships are designed to fit a variety of constraints, which varied massively between the combatant nations. These included where battles were expected to take place, what the ships were expected to fight, how much money was available, and the limitations imposed by various treaties.

An interesting example of this is in submarines. The British expected that advances in anti-submarine warfare would make classic submarine tactics impossible, and require smaller submarines to defeat. They also had to deal with the strict limits on size resulting from the 1930 London Treaty. This resulted in the construction of the T-class of submarines, with 10 forward facing torpedo tubes on a displacement of 1090 tons. The exceptional forward armament was expected to be necessary for long range shots based solely on SONAR information, which would be forced by developments in ASW capabilities. The smaller U and S classes were built to similar constraints. The Germans saw their submarine fleet as operating for short patrols against convoys. They were designed with large torpedo storage, but relatively small fuel storage. They also had poor accommodation for the crew, as they weren't expected to be on patrol for long periods. The US Navy wanted longer ranged, higher speed submarines for fleet operations in the Pacific. This meant they built far larger submarines than the British or Germans. Using expertise from the railway industry, they developed compact, powerful and reliable diesel engines for them. They also emphasised habitability, with air conditioning, water evaporators, and ice cream machines being fitted. The Japanese built similar sized submarines to the US, for similar reasons. These were intended as scouts for the battlefleet, and so several were equipped with floatplanes for scouting purposes.

Carriers had similar differences. The RN expected to be fighting in the North Sea, the Mediterranean or the South China Sea. As these are all relatively enclosed sea areas, it was thought that battleship engagements would be the norm, and hence the carrier was expected to play a secondary role. Carriers were given an armoured flight deck to protect them in such engagements. This limited the size of lifts and the height of hangars, reducing the size and amount of aircraft that could be operated from them. The RN was also extremely careful about fire, with aviation fuel tanks being heavily protected. The Japanese also built their carriers with closed hangars, but without armouring the flight deck. This made the ships lighter and easier to build than an open hangar design, as stresses were lessened due to the deeper hull. The USN had the hangar deck as the strength deck, accepting the trade offs in terms of weight for the ability to launch larger strikes and ventilate the hangar of fumes. It made damage control easier, but fires were also easier to start. The Germans never finished their carrier, the Graf Zeppelin, but she was expected to operate alone as a commerce raider. This resulted in several unique features of her design. She mounted 16 6" guns, more than any light cruiser. She had small, closed hangars, with an armoured flight deck.

Battleship designs saw a profusion of competing ideas. These included the so-called "all or nothing" designs of the British Nelson class and the French Dunkerque and Richelieu classes. These designs had the main armament clustered forward of the superstructure, and hence a reduction in length. This meant that the important areas of the ships were easier to protect for a given weight of armour. However, they had issues with blast damage from the main armament firing and were less able to fit the profusion of light AA weapons required later in the war. British battleships were generally expected to be fighting near a naval base, and had smaller fuel bunkers as a result. They were also limited by the naval treaties - the Nelsons made major compromises in speed and armour to fit 16" guns on the displacement allowed by the Washington Treaty, while the King George Vs were limited to 14" guns by the 1936 London Treaty. German battleships emphasised survivability, due to their role as commerce raiders. However, they had poor secondary armament. American designs were highly capable, with an excellent protective scheme and a hull form designed for speed. The Japanese built the two Yamato class super heavy battleships, with 18" guns, but had to accept poor armour, especially outside the central citadel.

Sources:

Nelson to Vanguard: Warship Design and Development 1923-1945, David K. Brown, Seaforth, 2012

Shattered Sword, Jonathan Parshall, Anthony Tully, Potomac, 2008

Jane's Battleships of the 20th Century, Bernard Ireland, Collins-Janes, 1996

The Kriegsmarine and the Aircraft Carrier, Marcus Faulkner, War in History vol 19 no4, November 2012.

To expand a bit on the differences between American and British carriers.

The USN's carriers were in general larger. The Essex class topped out at almost 28k tons of displacement, while the comparable Illustrious Class was only 23k tons with about 1/3 fewer aircraft, though this was partially a tactical decision as the British ships hangars were as big as US carriers. But they did not keep planes stored out on deck as a choice. Which is understandable when operating in the North Atlantic, but not as big an issue in the central Pacific.

The greatest difference though was the armoring of the flight decks in the RN. In the USN the strength deck and armor was the hanger deck protecting the important machinery, fuel, and munitions below. While the RN attempted to protect any bombs from coming into the crowded hanger area.

Realistically it had very little impact, US carriers relied on their AAA, and airwing, and escorts for protection, and wooden flight decks could easily be repaired. While sustained hits to the armor actually weakened the structure of RN carriers and in a few cases caused them to be scrapped early to avoid the cost of repair.

Another important difference was that virtually all USN capitol ships, and even cruisers from 1942 on were equipped with radar. This was not the case for the IJN, and was a major advantage in both patrolling, and directing gunfire. In particular it allowed the US to overcome the intense training that the Japanese had invested into night fighting. And as a general rule IJN ships were equipped with a greater number of torpedoes than their counterparts, the torpedo was seen as an integral part of their tactics.

Good Sources: Neptune's Inferno

Pacific Crucible

are good introductory reads I would point to.

The only example I can think of right now (please excuse the shortness of this answer, I'm on mobile) are the Italian Zara-class cruisers, which were designed to outspeed their French counterpart at the expense of their armour; however, the speed gained was not enough to justify such a design and subsequent additions further slowed these ships down to a performance comparable to that of other similiar vessels.