The F22 is more modern and advanced but in midair dog-fighting scenarios the Superhornet has been known to target the F22. The best pilot in either would win.
In my opinion the F22 would win. Although the Superhornet is an extremely good challenger, the F22 is a tested and proven machine with more stable results.
If these two jets were in a dog-fight with out a doubt the Superhornet would win. Thanks to superior turning radius and technology installed the battle would not last long.