The 625 should be on par with the 920 for battery life, because they both have 2,000 mAh. The screen sizes are very similar — I have held the 920 (4.5 in.) in hand with a HTC One (4.7 in.), and the One’s screen barely looked larger to me. Also based on what a lot of reviews are saying, the 625’s screen isn’t that great nor does it have the useful sunlight readability that the 920 has.
When it comes to storage with WP8, I’d say pick the phone with the largest internal memory because app data can’t be installed on an external MicroSD card. I have a Lumia 820 and I probably could have lived with 8 GB, but it filled up fast after downloading apps and games. I was forced to buy a card just to save my photos, videos, and music. Also at least with my 820, I’ve noticed that performance when the phone is accessing that storage can take a hit if you don’t buy the right type of card.
The Lumia 625 also only has 8 GB of internal storage, and I think it comes down to whether you’ll use the device more for apps/games, or for music and media. If you’re not a big app person or gamer, the Lumia 625 will probably be fine and you can dump all of your media onto a external card. But if you think you might end up using a lot of apps or playing a lot of games, trust me when I say 8 GB isn’t going to cut it. (Plus if you are a gamer, you should avoid 512 MB RAM phones because several big-name titles are incompatible, and the ones that are compatible I often hear complaints about running poorly.)
Also you say you care enough about taking pictures to want a good camera experience. The Lumia 625 uses a 5 MP camera that reviews say is just ok. Meanwhile, many users on here will tell you that the 920 is a great camera that has only improved over the last couple of months. The decision for this might come down to how often you may find yourself taking pics in low light, because the Lumia 920 will absolutely slay the 625 in that aspect.
Ultimately, you should try to get both in your hands and compare them. Sometimes, it’s just a matter of preference, especially because some people don’t like the added weight/thickness of the 920 versus other phones.