The question is obvious - so here is my answer at least:
When you use feedburner - feedburner & google essentially own your readers because you direct all your subscribers to your feedburner url, instead of your feed's url.
Why is this a bad thing?
Think about it - what if feedburner is discontinued tomorrow or becomes a paid service. What if something goes terribly wrong with the way feedburner parses your feeds and as a result you lose readers (has happened to many including myself).
You have NO control over your feeds and no control over your readers.
If you have your readers subscribe to the feed hosted on your own server - you still keep all our hard earned readers even after system changes, policy changes, upgrades etc.
Also - try serving ads on your feedburner feeds - not a pretty sight...
Why would you just hand over your list of readers to Google? So that you could have a couple of graphs and buttons on your site?
Why is everyone so brainwashed by Google?
So, to finish my rant - does anyone have a solution for this?
How to add stats to feeds, add bookmarking options etc without giving Feedburner control of your hard work?