The cost difference may reflect the performance difference.

I'm assuming you meant the RX 9060 XT? It is significantly more powerful than the B580.

I'd say the AMD card is the better purchase - it's more powerful and the drivers are well established with lots of support online for solving issues with specific games with Proton. Most of the time things just work but to be using a card and platform that is widely used makes life easier.

It's great Intel are supporting Linux and there is more competition in the graphics market, but I personally wouldn't suggest being a pioneer buying their cards. You're already doing something a bit unusual by gaming on Linux (even if it's growing rapidly). I wouldn't throw a new relatively niche card into the mix for now. It'd probably be fine but I'd stump up the extra cash for a better card that might last you a few years longer for AAA games.

AFAIK the B580 would only be a moderate upgrade for you, the 9060 XT would be the bigger jump, likely worth the extra cost.

If you want to go Intel, I'd say wait for the B700 series. The B500 series has proven a decent budget gaming card, but the 9060 XT is a solid midrange card and will be a lot faster than any B500 card.

Take a look at Phoronix https://www.phoronix.com/review/intel-arc-b580-graphics-linux/4
I think you are looking at two cards of very different capabilities

EDIT: unless you mean 9060
https://www.phoronix.com/review/radeon-rx-9060xt-amd-linux/2

Never had the opportunity to try an Intel GPU but from what I've looked they are good affordable low-end GPU for the value. However I don't know how the Linux support is. Also the AMD RX 9600 XT is a mid-range so not the same competition. I would say that if you can afford it you should upgrade to this one.

I just upgraded to the RX 9070 xt and could not be happier. I am get 150+ fps in cs2 and have had non issues with any other game or system.