We prefer suPHP for Joomla.
Not so many problems with 3rd party Extensions and quite many setup's fail with FastCGI but not with suPHP.
Suphp is very slow and wastes resources by starting a new php interpreter for each request. If you enable suexec, then fastcgi behaves similar to suphp an no extension should fail. I guess your customers will appreaciate it when their sites get much faster and you need less servers to serve the same amount of pages. You should give it a try.