SH3 is not without its flaws, but I'll try to give you a rundown.
SH3 was the first subsim to have a 3D crew. SH4 and 5 do that better, but ten years ago it was a true wonder, and despite comments on how dated they look that wonder still hasn't worn off for most of us.
SH3 was the first subsim to feature crew management. Most of us turn that off, as the way it was done was unrealistic and SH4 does it much better. But that's a negative, and you didn't ask for that.
SH3 was the first subsim to allow the player to sail through the harbors. It's another thing that SH4 could do better, but what makes it great is the improvement brought by various mods, and SH4 has none of those.
That brings me to may main point. What's best about SH3 is the way it's been modded. SH4 could have received the same treatment and ended up being much better, but it came to soon on the heels of its older brother and the modders who could have made a difference didn't want to touch it. They also were less interested in an American Fleet Boat game, and by the time the U-Boats Add-On was out a year later they were even less interested.
SH3 (modded) is the only subsim that gives the player more than 100 different merchant types to look at and shoot at.
SH3 with SH3 Commander is the only subsim that tells you the name of the ship you sank plus the cargo and crew numbers involved.
I'll be honest. If there had been a GWX and a Commander for SH4 I wouldn't bother looking at SH3 again. SH4 is, in theory, that much better. But there aren't, and that leaves the better base game without any of the extra added attractions that make SH3 perhaps not as good as SH4, but much greater in the end.
I continue to play both, for the above-listed reasons.