My wife and I finally upgraded to new phones yesterday (well, mine is completely upgraded; hers had a problem and will finish tonight, hopefully).
I was most looking forward to the extra CPU power. Threes went from a five-ten second startup to virtually instant, which was awesome.
Touch ID, I'm still trying to figure out. I thought (I had specifically asked someone at an Apple Store about it) that you could designate, on a fingerprint-by-fingerprint basis, whether it was usable just for unlocking, or for unlocking and purchases. That doesn't appear to be the case, but it's certainly easier to use that than to input a PIN.
There are a couple things I'm still figuring out with the camera (my pano attempts haven't been panos at all). I just sync'ed the new phone, downloading pictures, and that helped me figure some stuff out. We'll see if I'm right when I finish with that.
But I love the better lens, that's both faster (f/2.2 v f/2.8) and wider (30mm vs 35mm, film-equivalent focal length (really 4.12mm vs 3.85mm, remembering the 15% increase in sensor size). I haven't yet cared about the extra megapixels (the iPhone 4 is a 5MP, vs 5s@8MP), though that'll be good to have. The 1080p video will matter, but hasn't yet. I really like the idea of the slow motion video, but I wonder whether I'll really use it.
I also went from 16GB to 32GB, and that's a big win. I've been having a lot of trouble with space, which has been impacting both apps and photos, and now I've got a ton of space. Loving that. I just need to remember not to do something like, "Well, let's dump a lot of stuff in there, since I've got the space".
Similarly, I was having trouble with icon space on the desktop, so I love having an extra row. I had just had to do some trimming a few days ago, and now I don't need to have done that. Ah well.
Going from 3G to LTE will also end up being a big win, although it hasn't mattered yet. Looking forward to taking advantage of that (especially once iTunes Match finishes doing the matching. In the eight or nine hours since I mentioned how slow it's going, it hasn't shown any sign of advancing).