I prefer Nginx for easier rewrites and PHP-FPM is quite usful for large sites, as the PHP processes are dynamically created. Lighty runs php-cgi as fastCGI and its static. To be honest Lighty and Nginx are very close memory and CPU wise, but I prefer Nginx+PHP-FPM. Lighty gave me quite a list of trouble when it came to rewrite rules with Joomla, had to use LUA for it. Also Nginx has a native module for Memcached which is quite helpful. Static files are good, but reading from memory is even faster given the situation. I think Nginx is good with long-polling and can run as a push-server.
I will try Lighty's SAPI config sometime soon and see how it can perform. As for PHP Optimizers xCache is superior to APC for memory. ON a test server with XenForo it gave around 500KB difference per page load. Seems small but its actually quite a bit.
I'll try to enable XCache. The problem with FastCGI is that op-code caches, such as APC and XCache, just don't work, since they rely on shared memory, between the PHP processes.