The performance will be very similar. In the one scenario you use FastCGI as the communication layer between Nginx and PHP and in the other scenario you use Apache + HTTP as the communication layer. Ultimately the difference between FastCGI and HTTP is not likely to make any difference when you have the overhead of PHP to factor in. Apache will use some extra memory but since it keeps PHP embedded within its own process the speed difference is minor.
Ultimately you should disregard the above unless you really seriously absolutely must have the utmost performance from one server as you are stuck in a location with only enough power for one server, thus making it impossible to scale at all.
The important aspect here is what you're comfortable with and features you require. If you're comfortable with .htaccess then figure out if getting rid of the Apache memory use, the performance hit of .htaccess and the added features of PHP-FPM is worth the investment it is to relearn stuff.
In case it's not obvious I'm a fan of going straight Nginx + PHP-FPM, mostly because of neat features such as the slow-log which provides me with an extra way of making sure everything is working as should be. But it does require relearning, there is no way around .htaccess no longer being available, you cannot magically convert your .htaccess file to nginx format as the nginx configuration is significantly different.
If you do decide to go with Nginx then do yourself a favour and read the documentation. Specifically my nginx primer written as an introduction, the official English documentation from nginx author Igor as well as the wiki directives on location and try_files.