Apache + mod_wsgi / Lighttpd + wsgi - am I going to see differences in performance?
Apache...
Apache is by far the most widely used web server out there. Which is a good thing. There is so much more information on how to do stuff with it, and when something goes wrong there are a lot of people who know how to fix it. But, it is also the slowest out of the box; requring a lot of tweaking and a beefier server than Lighttpd. In your case, it will be a lot easier to get off the ground using Apache and Python. There are countless AMP packages out there, and many guides on how to setup python and make your application work. Just a quick google search will get you on your way. Under heavy load, Lighttpd will outshine Apache, but Apache is like a train. It just keeps chugging along.
Pros

Wide User Base
Universal support
A lot of plugins

Cons

Slow out of the box
Requires performance tweaking 
Memory whore (No way you could get it working on a 64MB VPS)

Lighttpd...
Lighttpd is the new kid on the block. It is fast, powerful, and kicks ass performance wise (not to mention use like no memory). Out of the box, Lighttpd wipes the floor with Apache. But, not as many people know Lighttpd, so getting it to work is harder. Yes, it is the second most used webserver, but it does not have as much community support behind it. If you look here, on stackoverflow, there is this dude who keeps asking about how to get his Python app working but nobody has helped him. Under heavy load, if configured correctly, Lighttpd will out preform Apache (I did some tests a while back, and you might see a 200-300% performance increase in requests per second).  
Pros

Fast out of the box
Uses very little memory

Cons

Not as much support as Apache
Sometimes just does not work 

Nginx
If you were running a static website, then you would use nginx. you are correct in saying nginx's mod_wsgi isn't suitable.
Conclusion
Benefits? There are both web servers; designed to be able to replace one another. If both web servers are tuned correctly and you have ample hardware, then there is no real benefit of using one over another. You should try and see which web server meets your need, but asking me; I would say go with Lighttpd. It is, in my opinion, easier to configure and just works.
Also, You should look at Cherokee Web Server. Mad easy to set up and, the performance aint half bad. And you should ask this on Server Fault as well.
I'm a newbie to developing with Python and I'm piecing together the information I need to make intelligent choices in two other open questions. (This isn't a duplicate.)
I'm not developing using a framework but building a web app from scratch using the gevent library. As far as front-end web servers go, it seems I have three choices: nginx, apache, and lighttpd.
From all accounts that I've read, nginx's mod_wsgi isn't suitable.
That leaves two choices - lighttpd and Apache. Under heavy load, am I going to see major differences in performance and memory consumption characteristics? I'm under the impression Apache tends to be memory hungry even when not using prefork, but I don't know how suitable lighttp is for Python apps.
Are there any caveats or benefits to using lighttpd over apache? I really want to hear all the information you can possibly bore me with!