It works fine.  Design-a-Course (from my signature, the product I
maintain for a living) runs on Tomcat under SSL.  We've had no problems.  
It's a little more of a hassle to update the certificates once they
expire, since you have to generate a new CSR.  Overall, though, it's
pretty straight-forward.

I'm sure that it depends on context.  I've definitely seen Apache (2.0
IIRC) perform faster than Tomcat under very heavy load.  The 1.x release
cycle used to suffer from fairly serious performance problems under high
load, though.

I think there are several reasons besides Apache's slowness that
everyone claims to be faster than Apache:

- Apache is the de facto standard web server, running on a fair majority
 of servers, so a lot of servers go out of their way to establish
 advantages over it.

- Tuning plays a big role in performance of something like Apache.
 Proper choice of filesystem and various parameters can be used to make
 anything faster than anything else, so it's easy to establish being
 faster.

Of course, I'd recommend anyone do some load testing if they are seeing
high enough load to care whether they're getting optimal performance out
of the web server.