SH3 = Older, therefore has much more polished mods, most of the problems are fixed by said mods/updates. Being old is also its disadvantage though. Max resolution is 1280x1024, which was fairly small even when the game came out. Graphically its still nice.
Oh, and it has U-Boats in the Atlantic, which is always a guaranteed winning formula. Game is very difficult and challenging since the Germans were historically the underdogs.
This makes the game a lot more fun to play, and it can get very tense sometimes.
SH4 = Newer, fewer mods, more bugs. I guess the developers tried to streamline the game a bit to make it more accessible, but I personally prefer SH3's interface. Some nice graphical features (like post-processing, etc) has high res and wide screen support.
As far as the setting goes, its set in the Pacific Theatre of Operations, which means you get to play with American Fleet Boats. A lot of people don't like this, I personally do (I have since SH1).
Also due to it being newer, it has higher system requirements, but most decent systems today should be able to run all settings on full without any problems.
Unfortunately it seems as if Ubi basically started working on SH5, and hence stopped developing patches for SH4 far too early, since as I said before, it has a lot of bugs which will probably never get fixed.
Verdict: I would love to give SH4 a try with some of the mods (RFB, TMO) but I'm having trouble getting it all to work flawlessly, but I am really spoiled with SH3 and the excellent job the guys have done with GWX3.0, if only it had high resolution, I'd be totally set with SH3.
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