I also upgraded from a 4S to 5S, and I never had any issues with iOS7 on my 4S. The battery life was always great and I could easily go a day or two of casual use without draining the battery. I never noticed any lag or anything either. I got my 5S before the 7.0.x incremental update came out that fixed the transition effects, so I'm sure it's even better on the 4S now.
Overall, my 4S was always fast, so I haven't noticed any speed difference between it and the 5S. Battery life is probably better on my 5S since it has a bigger battery and it's brand new vs 2 years old.
Hard for me to say since I went from Sprint, which has an un-usable data network, to AT&T which has an amazingly fast 4G network. I definitely use my 5S more since the data network actually works.