It really depends on what you want from the game. If gameplay is the only factor then the 23-year-old Aces Of The Deep is still the best.
Okay, now that that's out of the way...
SH3 was the first subsim to actually have a crew on board the boat. Not only animated crewmen on the bridge and in the control room, but the names of the crew appearing in the boat's roster. The super-duper mod SH3 Commander, among its many cool features, adds a database consisting of most of the 40,000 U-boat crewmen who served during the war. Divided into first and last names it creates a possible 1.7 billion crew names. That's not really a big deal, but nothing like it has been done for the newer versions.
One of the complaints about SH3 is that you have to move the crew around as they grow tired or else shut off the fatigue altogether. SH4 fixes that, with the crew rotating themselves. SH5 goes a step further and removes the crew altogether. I hate that, but that's just me.
SH3 was so new and so different that a whole lot of modders went to work on it, and some still are twelve years later. SH4 came out just a couple of years later, but most of the modders weren't interested. Part of that has to do with the fact that SH4 is based on the American submarine war in the Pacific. I find those complaints to be funny, because the original Silent Hunter was also based on the Pacific War. Besides that, there is a brilliant mod that lets you play German U-boats in the Atlantic, just like SH3.
One of the coolest things about SH4 is the 'General Quarters' function. Normally only 1/3 of the crew are on duty, but if you call battle stations the entire crew goes on duty. Not only that, but efficiency is increased by automatically having the senior man at each station take over. Just remember to cancel the order when the fight's done or the crew will stay there until they all fall asleep.
SH4 is so good that the only thing stopping me from replacing SH3 altogether is the lack of the great mods that exist for SH4.
SH5 is visually far better than its predecessors, but it has certain failings. I won't go into most of them because they have mostly been fixed by great mods. They aren't the same mods I like for SH3, so I stick with the oldest one. A lot of people disagree, and love SH5, so arguments against it are mostly personal in nature.
All are good. As I said at the beginning, it really depends on what you want from the game. I continue to play SH3 simply because the mods I like best are only for that game.
On the other hand they're all pretty cheap, so it wouldn't be hard to start a collection and then decide which one you think is best.
