Touch controls are better on the phone.

Personally, I prefer playing with buttons, but I'm old like that.

I have it on both and they're pretty much identical. Having buttons available can be sorta nice for specific actions, but on the other hand a phone is easier to carry around. Both are great with minor pros and cons.

It's the same experience, imo. On mobile, you can drag and drop the cards into a buy/sell/use section; on the steam deck, there are Xbox control indicators to buy/sell/use/select. I haven't noticed any other differences. Google play keeps a save file in the cloud, like steam.

Edit: my bad, on Mobile, seeing the tags at the bottom of the Select Blind window is a PAIN because, to see its description, you have to press and holto read it, then slide your finger away to be sure you don't select it. The tag icon is small. If you release your finger while over the tag icon, the tag is selected.
A Tag is a bonus you can get if you choose to skip a Blind (which is a term for one round of playing your cards). It's usually more profitable to play the Blind than pick the tag.

I prefer to play it on mobile (pirated it to try it out) but I bought it on Steam. As much as I like the mobile version I really don't want to kill my battery.

Like the others have said, it's pretty much identical. What makes it perfect on mobile (imo) is dragging the cards feels more natural (especially being a board gamer).

I haven't played it on mobile, but it does seem made for it. And everything is turn based with absolutely no timers.