The only noticeable difference today is DLSS vs no DLSS. If you would use DLSS in the games you play, then go with the 4070. DLSS is just significantly better than FSR, at least at resolutions lower than 4k.
Also the 4070 has slightly better RT, but I don't think most people care much about that.
In the future the 16GB VRAM of the 7800 XT might become an advantage, though the difference between 12 and 16 is not huge. And the 7800 XT is like 3-5% faster. Due to the higher memory bandwidth it will probably also age a little better.
So if you think you won't use DLSS, definitely go with the 7800 XT.
This is assuming they are priced as they are right now (4070 is ~520 and 7800 XT is ~500). If the 4070 costs 15+% more money, just get the 7800 XT. Or spend a little more and go with the 7900 XT on sale (I've seen it go for $700, might go even lower on BF).
https://jarrods.tech/list-of-laptop-battery-life/