HHVM has a built in Server, Proxygen. You can run HHVM with the Proxygen server or run it in FastCGI mode, using another server such as nginx or apache to handle web requests.
I cannot find any benchmarks or authoritative source that provides any indication of which of the two option performs best. Obviously I could provision two systems an manually test various loads under different concurrency combinations and put together a benchmark, but I'd rather avoid the work if someone has already done such a comparison.
Does anyone know in general which is the better option from a sheer performance standpoint?