What is the difference between feeds served by my WordPress install vs feeds served by FeedBurner?
How to disable hosted Wiordpress feed completely and use feedburner?
Here are some reasons I think FB does well:
Some of above features you can do with plugins, but it costs CPU usage and sometimes host space. With FB, you let FB do all of these stuff without any prices.
FB has its own plugin that redirects WP feed to FB automatically, you can find it in FB.
FeedBurner provides stats that WordPress does not, such as analytics. Here are some uses of FeedBurner features:
Out-of-the-box, WordPress feeds work fine and do just what they're supposed to do.