https://www.videocardbenchmark.net/compare/4369vs4917/Radeon-RX-6700-XT-vs-Radeon-RX-7800-XT
You can expect about a 20% better performance. You also have 4GB more of RAM which supposedly is good for future-proofing but only a few games and applications can even use more than 12GB right now. I don't expect it to be the norm anytime soon.
On the Linux side you should check to see if people on RX7000-series have resolved any initial issues with graphics drivers, since I've often heard reports of problems when AMD graphics cards are fresh out of release.