All of the features you list are supported by Nginx out of the box:
We use a gross combination of Lighttpd, Apache and Nginx at work. We can't get rid of Apache entirely because we're running a couple custom modules for it (a hacked mod_pubcookie, among others) and it'd be a pain to port them over to Lighttpd/Nginx.
I used to use Lighttpd as our de-facto lightweight content server, but have hit numerous snags with its FreeBSD implementation (it seems to break when using FreeBSD's sendfile/kqueue syscalls - and when it breaks it takes the whole server down with it). I've never had any issues with Nginx, and have been slowly replacing all our Lighttpd installs with it. Nginx has been rock solid in our deployment.
The one issue that I have had with Nginx is that its documentation isn't well-indexed by Google, so you have to go directly to their site to look up stuff. Despite that, all the documentation is organized in a manner which makes sense to me, so it's not too hard to find what I need.