RSS: self hosted vs feedburner?

I've been working on getting RSS feeds working for a small personal
project of mine. In my research to see what/how other people were doing
for RSS, I noticed that a vast majority of blogs seem to be using
feedburner to host their feeds. Personally, I prefer to avoid becoming
dependent on third party tools as much as possible.

So far, I've got the basic locally hosted feed working, supporting the
Last-Modified/If-Modified-Since headers to save on bandwidth and cut
down on unnecessary database hits. But am I missing some obvious
advantage that using a third-party host provides, or am just asking for
trouble by hosting this myself? Or is it simply that so many people use
feedburner because that's what everyone else uses?

The major pros and cons for self hosted vs feedburner implementations
from those with experience would be appreciated.

I don’t know about anyone else but I mainly use feedburner for the stats they offer and the fact that the feed URL will remain the same (without me needing to add any rewrite rules) if I move things around on my site.

Of course, the fact that it reduces bandwidth usage quite a bit is nice too, but it’s a secondary concern for me.