Hello! Yes, there were extreme differences on the beachheads in actually all of the things you questioned. I'm personally only comfortable in answering in regard to the American beaches, as I am not familiar with the British and Canadians to be able to go into the level of detail that I would like, or that you deserve. However, Omaha Beach was the bloodiest beach and the most difficult out of the five. I feel fairly confident in that statement and I don't intend to disparage those who landed on Utah Beach and I recognize that all of them were better men than I, and most definitely more courageous than I could ever be.

That being said Omaha Beach is largely considered the bloodiest and toughest beach for soldiers to have landed on. Part of this is because Allied planners expected the defenders to be a battalion made up of a mix with up to 50% being non German conscripts (mainly Russian volunteers if I recall). There was a capable fighting force (a division strong) about 20 miles inland, and the Allies expected that they would be committed to the counter attack but not be on hand to repel the invasion itself. Well, Rommel commanded in early March that the division be moved forward to the sea as part of his plan to stop the Allied attack on the beaches and to push them back into the sea. The Allies actually learned of this reorganization on June 4, but this was way too close to the invasion date, which they couldn't push for a variety of reasons, so the invasion plans were left in place. This meant that resistance was much stronger than expected and severely blunted the Allied advance.

Omaha Beach was also incredibly bloody because of the fact that so few of its plans materialized (as you put it) correctly. Ten of the boats sunk before the shore and the ones that weren't had to deal with fog and smoke completely obscuring the shoreline so that navigation markers weren't visible. This meant that out of 9 companies that landed during that initial assault wave, one company landed where it was supposed to. In addition to this all of the companies experienced much heavier resistance than was expected because the arial bombardment completely missed its German targets. The pilots were told to take an extra ten seconds before they dropped their bombs in an attempt to avoid hitting the landing craft. These ten seconds translated into the bombs hitting literally miles from their intended targets.

As the Allied soldiers disembarked from their landing craft, they quickly discovered that, surprise, since everything else had been going so well, they were landing on sandbars anywhere from 150 - 300 feet out from shore. As the men struggled through this distance, they had to wade through water that was neck deep at a walking pace because of how heavily loaded with gear they were. Then once they finally made it to the shore, they still had about 600 feet to go in order to make it to cover. The Germans took advantage of this and cut the American soldiers utterly into pieces. The companies in the best shape were disorganized, (because of how off course they were and disoriented as a result)leaderless, (their leaders had for the most part been cut down during the landing) and pinned down under heavy fire.

The second wave of assault troops landing on Omaha Beach began to come in at this time and they faced the exact same challenges of the first wave because the first wave had been unable to clear a bit of the way nor able to lay down covering fire for the second wave. Along with the second wave of assault troops, there were also a number of engineering teams trying to land and they experienced the same difficulties as the assault troops. In fact there were a couple of engineering teams that came in in areas where no assault troops had landed, which meant they were the primary targets for the German defenders there. Regardless of all of these difficulties the engineers began their work of clearing obstacles on the beach. This task was made doubly difficult as the German defenders began to destroy their equipment and supplies and the assault troops tried to use the obstacles for cover from the onslaught of German fire. All of these challenges aside, for all their work, and their casualty rate of 40%, the engineers managed to clear 6 paths on Omaha Beach.

Another reason that Omaha was so bloody was because of a lack of supporting heavy weapons and vehicles. This happened because so many had been sunk on their way in, so with a few key exceptions (several tanks and a few heavy weapons squads) soldiers could only fight with what was on their back. The necessity of seizing the natural pathways up the bluffs meant that the Germans had focused their defenses there. This in turn meant that the American soldiers who landed in areas with no natural pathways up were able to fight against less, although still fierce resistance and begin to build up troops there. These troops were still disorganized, leaderless, demoralized, and pinned down by heavy fire, there were just more of them there.

However they did have a single advantage in the form of naval bombardment. The navy was ordered to sail in as close as possible to the beach and to open fire on opportune targets. I want to relay one of my two favorite stories of D-Day here, with the USS Frankford. The destroyer steamed in and began cruising back and forth along the beach, opening fire at targets. They were nervous about hitting their own troops however, that all changed when the crew saw one of the few surviving tanks immobilized on the shore yet noticed that it was still firing. They then began to carefully watch where it's shots hit, following each of them up with a barrage of naval artillery.

The task of getting the men to assault the bluffs then fell to individual leaders (NCOs and Junior officers) separated from their units, and to average soldiers who saw what had to be done and bullied, insulted, and motivated the soldiers around them to get up to those bluffs, scale them, and start working on the German defense. "Are you going to lay there and get killed, or get up and do something about it?" was how one lieutenant motivated his men to start moving up. The process was slow, bloody, and painful, with soldiers breaking through the defenses in small groups and continuing the fight up on and slightly beyond the bluffs. The intensity of the fighting and the tenacity of the German defenders meant that at the end of the day, the Americans at Omaha Beach had made pushes of various extent, at their greatest a mere mile and a half in from the beach. This Map wil help you visualize just how little the American foothold had penetrated.

Compare this on hand to the other American Beach, Utah Beach. On Utah Beach, infantry and their supporting tanks, vehicles, and heavy weapons landed in waves quickly securing the beach with minimal casualties(Out of the 21,000 troops landed, they suffered under 200). However they too were swept off course, with the advantage of missing the more defended original landing locations. Brigadier General Theodore Roosevelt Jr. (Yes son of the Teddy Roosevelt) decided that that was perfect and quickly organized his men and effectively made this the new landing area with little confusion if any. As this was going on, engineers began clearing the area of obstacles and additional reinforcements continued arriving. The soldiers at Utah Beach did however only capture about half of what they planned to. This area was relatively secure and a vital foothold for the Allies.

Edit: Completely forgot about the book recommendations, I really am a huge fan of Max Hastings and think his book Overlord: D-Day and the Battle for Normandy would be helpful here. My other recommendation would be Omaha Beach: D-Day, June 6, 1944 by Joseph Balkoski