chx shared an interesting article via his Twitter feed today; some speed comparisons of Apache with the mod_php extension (which embeds the PHP interpreter into Apache for faster but less-secure execution) versus Nginx and PHP via FastCGI.
The author's conclusion was that, just in terms of serving PHP, Apache is faster if you disable the feature which looks for .htaccess configuration files in the web root directory and child directories, which slows things down a lot. But, "If you are running mixed content, such as adding CSS, JS and images, then NginX will provide better overall performance but it will not run PHP any faster."
Is there really such a thing as a web server which only serves PHP and no images or other files? I suppose if you use CDNs for everything… For me, I can't afford CDNs, and have other reasons for not wanting to use Apache (central being the desire to keep resource usage low on my tiny VPS account), so I guess I'll stick with Nginx for now.

Comments
Run PHP-FPM.. This
Run PHP-FPM.. This essentially turns PHP into its own service independent of the web server.. So effectively a PHP only server that the web server passes PHP processing requests to..
While I have not benchmarked it you probably get the speed of mod_php without the overhead and really granular control over PHP processes.. I found it to be a winner all round..
apache worker & php5-fpm is an option
Foreword: if you're doing the work nginx & php5-fpm is the way to go based on the amount of very good information out there on running any php app in this manner.
That said, you can get performance that is on par with nginx & php5-fpm by using Apache MPM Worker to fastcgi, just like nginx does. Just be sure to do like everyone else and disable .htaccess files or your performance gains will be hampered if you choose to, or are forced to go this route.