I don't know about php-fpm, but the old fastcgi implementation was extremely buggy when we tried that with lighttpd back when there was no nginx yet.

Burned like this, I'm currently using Apache/mod_php for all dynamic content but let nginx serve the static files (using a reverse proxy configuration. Turn off KeepAlive in Apache!).

This works extremely well and totally stable.

Even though php/fastcgi is now a more common configuration than it was back then, mod_php is still more common and hence better tested.