I currently use them both and Redis seems faster but I just started using it so i really havnt set up any mail services or cart/check outs and working reviews/comments, My main site uses FastCGI and I have no complaints its been challenging getting the caching set up to my likings and i like a challenge so i choose FastCGI just because i have been using it for some while and its been super dependable. Gud luck with your decision they are both superior solutions.
Best Regards!