Earlier, nginx was used to handle just static content and passed the php stuff to apache httpd. These days people just use php-fpm instead so nginx can handle everything in a php based stack without needing apache.
Using mod_php with Apache IS faster than PHP-FPM, however, it uses MUCH more RAM. In a RAM constrained environment like a VPS, it simply isn't an option.
The latter part is simply not true - I run Apache with mod_php for a number of sites and web services on VPS's with little RAM without any problems, and that's alongside MySQL, Exim and SpamAssassin.
I don't have exact figures, but each site probably gets a few hundred hits/day, and the mail server probably gets hit every few seconds. The OP made a sweeping "not an option" statement though, not "on a popular site hosted on a VPS".
Nginx + php-fpm is MUCH faster than a vanilla apache httpd + php stack. The magic though, is not just speed. It's also the feature-set. I'm
working on a pyramid(pylons) project right now and will be using nginx to load-balance the wsgi server instances and to serve static content. I don't think I could use apache for that. The configuration for nginx looks neater as well (my personal opinion)
Benchmarks on my projects show that the difference is insignificant. Since I currently do not have memory constraints I am still using nginx + apache with mod_php.