Gamo makes some pretty serious air rifles now. I’d lean towards the .22 over the .177 caliber.
I’ve got a Gamo in .177 that kills squirrels out to about 30 yards. I’m sure a woodchuck at that range would be no problem, I’d just make sure I had a good broadside shot to the vitals. A .177 to the heart/lung area will put them down. I don’t think I’d try a head shot unless I was really close.
I don’t know the price on these guns. I got mine as a gift.