For a Switch Pro, I'd think there'd be modest gains in power. Certainly a bit of a bump to help with resolution and FPS, likely entirely backward compatible with the current Switch library and I'd imagine Nintendo would mandate that all games that play on Switch Pro will also work on Switch. In other words, a half-measure PS4 Pro kinda thing.
For a Switch 2, I'd expect to see major hardware revisions. Not the form factor itself, which seems to be doing very well, but in terms of compute. And, yeah, maybe a second-gen version of the joycons to iron out those kinks. Personally, I'd like to see faster load times and storage I/O. Admittedly, the PS5 and Series X have spoiled me here. I've commented before that it feels like playing on a cartridge, depending on the game. It's just jump-jump with no real loading to speak of. I recently went back to play New Pokemon Snap and I furrowed my brow every time I had to load in for new island hop. "Why is this taking so long?"
If Nintendo can provide me with faster load times and a resolution above 1080P and FPS above 30 (on the games I care about), I'd be a happy camper, regardless of which system it shows up in. If the rumors turn out to be true, it looks like the Switch Pro would do that via Nvidia DLSS.