Is Tomcat Native worth the trouble?
(Disclaimer: I've no data to back this claim).
I've found out that native Tomcat (APR) helps more with SSL/HTTPS. It still is a lot slower than, say, Apsis Pound doing SSL on a separate machine.
For static files, the APR seems to help with memory-mapping the static resource and makes things a little faster when in the order of hundreds of requests/sec, but then again the correct HTTP caching of static resources helps a lot more (since not so many requests for the static resource come in).
All in all, I don't think it's worth it, if you're going to compile everything by hand (you'd be out of Java-land).
If it's a simple apt-get install, go for it.
In any case, I'd invest more in Pound SSL termination or Varnish caching.