Dustcan
Dogs
There’s no functional difference between a laptop and desktop as far as performance for games. It’s all in the hardware.
And no, I am not the guy to talk to about which is the best hardware for which price.
For the most part choosing between a laptop or desktop amounts to portability. If you travel a lot? Laptops are easier to move. Otherwise desktops are technically better for heat dissipation: the more room means there’s less hot metal getting hotter from other hot metal crammed into a small space.
Regardless, if the problem is just a battery then replacing that is, obviously, far cheaper than a whole new rig.