I replaced my 925 with an 830 so I think I have a pretty good idea of the strengths and weaknesses of each. Which you prefer will very likely come down to what your needs are. Here is a quick summary of which does specific things better. Most of it is objective, some of it just my personal preference.
Form Factor: I prefer the 925's smaller size. They are the same width but the 830 is noticeably longer and slightly thicker.
Display: 925's AMOLED is richer and works much better in daylight. Glance is almost unreadable on the 830 sometimes.
CPU: 830 feels slightly slicker/faster but there is not much in it.
Camera: Both take brilliant photos, I couldn't pick which was better.
Speaker: 830 is the loudest phone I've ever owned, probably the loudest I've ever heard. You'll never miss a call.
Vibration: 925 is much better, it almost seems broken in the 830.
Storage: 830 wins, hands down.
Battery Life: Hard to tell (I'll explain below).
Build Quality: Both excellent.
The reason it's hard for me to say much about battery life is that I never had Quiet Hours on the 925, so I used to switch it to flight mode for 8-10 hours a night. But the 830 does have it so the radio remains on 24 hours a day. So for me, it felt like the 925 lasted longer but I suspect if I had been using Quiet Hours on it, it wouldn't have lasted as well as the 830. I suppose the take away from that is that they are both in the same ball park.
Here is the most telling, and by far the least objective thing - last month I dragged my 925 out of the cupboard to try out Windows 10 Mobile and I very quickly realised how much more I like it. With the Charging Shell on it, it looks fantastic. The screen is beautiful and works amazingly well in daylight (I'm an outdoorsy person). After deciding that I could live with all the issues with W10 Mobile, I have gone back to using the 925 as my daily driver. It's completely irrational but I love that phone and I don't miss the 830 at all.
I bought the 830 because of the microSD support - my music collection has outgrown my ZuneHD so I wanted to put a 128Gb card in the 830 and use it as my music player. I discovered that was a bad idea - the music stops whenever you get a call and I listen to enough music during the day that battery life became an issue. I ended up buying a new Walkman so the main thing I bought the 830 for became irrelevant. It is still a great phone and, ultimately, I really don't think you can go wrong with either so just buy the one you like the most. Don't worry about comparing specs or any of that other stuff because either will do everything you want/need to a similar standard, just get the one that you think will make you happier.