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.
Have you tried anything like Guild Wars 2 or Apex Legends? I don't have a huge list of games I play but if anything sticks out for games Wirth mentioning their pros and cons on them LMK. Are the key bindings for in game control on the Asus just a controller or is it more custom layout possible like the Steam Deck? I don't have either but I'm curious about them. Would be kind of nice to bring one on trips when the rest of the family is asleep I can quietly play. Or when on the couch.
The Rog Ally is going to be able to play just about anything with a decent framerate, the real issue is the controls.
When it comes to controls, the Ally is way more complicated to get setup that the Steam Deck. Here's an example...
I really wanted to play BattleBit on my Ally, it's mechanically deep Battlefield-esque game built with mouse and keyboard in mind with many, many controls.
The first issue is that the Rog Ally doesn't natively support the gyro it has, so I needed to install Handheld Companion to be able to access it, which required paying a Patreon sub, and also installing third party drivers for the gyro.
Handheld Companion is another control interface i have to configure, in addition to the armory crate controller interface because Steam doesn't recognize the rear buttons(the rog ally just broadcasts itself as a XB360 controller WITH NO XBOX BUTTON), then finally the steam input controller interface once I'm in game. It's far more complicated/awkward than the deck.
I was able to get a great control setup for the game and it's awesome, but it took probably 6 hours of combined research and configuration.