Crisis 3 will only really work well with Forever Evil
Crisis 3 is optimized to work best with Forever Evil, but should work perfectly fine with any other base set.
C-3 continues the theme's of "higher Destroy" and "VP Token's", but the set provides enough cards that do the above, and an optional rule to get more VP token's, so that any base set will work.
Things to note:
Crisis 2 Crisis-cards are arguably better balanced than Crisis 1, but C-2 does -slightly- continue the theme's of Heroes Unite, so a few cards may be flavor-fully out of place (like the -2- Power Rings).
C-3 Crisis-cards use the "Contribute" mechanic, which many feel is a better system than the old "all at once" approach of C-1 & C-2.