They definitely each have their own strengths and weaknesses, if I had to pick a winner, I'm going with Steam Deck, you just can't compete with their controller API and the Deck's assortment of input options; that alone makes everything else obsolete.
Raw horsepower(Rog v Deck) is a meaningless metric; Using the Rog is like driving a 911 without tires, just rims; you literally can't control it.
I have been considering a switch to the Ally. I agree that the Deck has more input options built-in, but there are several games I've been aching to play that aren't supported in Proton(and don't load on the Deck, I tried). I also would like to install Battle.net and play Diablo IV.
I realize there are hacks and workarounds to get a lot of things working on the Steam Deck, but I want to play games, not spend an evening doing Google searches and troubleshooting.
I know this literally contradicts your last sentence, but I got Diablo IV up and running on desktop Linux really easily and it runs great. I followed these instructions minus the ProtonUp-Qt part (Proton Experimental runs it): https://www.gamingonlinux.com/2023/03/heres-how-to-run-diablo-4-on-steam-deck/
It amounts to:
Yeah, but you can just install windows on the deck. OS compatibility arguments aren't really valid(no intentional offense), since at the end of the day.... these are just pocket PCs.
I will say tho, the switch is def the most limited. I think if you're in the market for a good handheld in 2023 and love Nintendo games, pick the rog(if you know your way around emulation)