I've found Lighttpd way easier to configure than Apache and am having it serve my static content simply because we don't need to worry about every little bit of performance just yet.
It does some magic sharing of read-only segments of memory by taking advantage of copy-on-write and a special version of Ruby, but other than that it seems like it does the exact same thing as FastCGI.
Well, it depends on whether you're looking at it from an academic or practical standpoint. AFAIK the technologies are not entirely dissimilar, as you suggest, but there are notable differences once you actually put them into use. I've used both for running rails apps, and a few things stand out for me:
1. Passenger is much easier to set up: it took me about 5 minutes to get my first Passenger based rails app up and running. The last time I set up a rails app w/FastCGI (admittedly a few years ago now) it took me much longer. This comes down to simpler configuration combined with better documentation. Subsequent application deployment is also easier (no manual server restarts required). This is worth a lot in practical terms, even if not flashy.
2. Passenger seems more stable. I never had quite the problems with FastCGI that others appear to have had, and I've only been using Passenger for a few weeks now, but there's a reason people used FastCGI less often once Mongrel became available.
3. Oh, and there's some neat stuff too: automatic spawning and pruning of application instances in response to demand, etc.
With Passenger, I set it and forget it. Time is money.
I've been using NGinx/Mongrel for most of my large deployed apps, but am working to get things moved to Passenger (and Apache, natch), simply for the ability to do a graceful restart on most code changes. For large apps, the ever expanding mongrel footprint and slow restarts is becoming too much to bear.
So for me, Nginx has a lot to offer over Apache, but with the rails deployments I've been working on mostly, it's no longer enough.
Our app is Python 2.5 and Django (well, kinda Django). I haven't gotten to deep into the Lighttpd thing yet, but it looked promising. Maybe I should take another look at Nginx?
Also, do you recommend FastCGI or WSGI? I've had a hard time figuring out precisely what the differences in implications are.
I also use nginx as proxy in front of apache and dev instances of django manage.py runserver (nginx serves up static, passes dynamic on to back ends)
Nginx is so powerful, flexible, and has never given me a single problem. I loves it.