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if Apache is tuned properly - by removing extensions that are not needed, and having an optimized configuration - then the performance can be acceptable. Apache is process-based while NGINX is event-based. NGINX is designed with Speed in mind and makes better use of RAM so you can squeeze more performance out of it without always needing caching or purchasing higher cost (more memory-based) packages.
Using [PHP-FPM + [URL="http://php.net/manual/en/book.apc.php"]APC (caching) + [URL="http://nginx.com/"]NGINX](http://php-fpm.org/) should allow you to increase performance without breaking the bank.