While you won't notice any difference on the public side of the Feedburner site, there are big changes once you login to view and administer your feeds. The interface is completely updated, and a big improvement in my opinion. Gone are the pop-ups (which I personally dislike) to access such features as creating "chicklets" (small banner) links to your burned feeds. You also have three templates, or themes, to choose from when offering your visitors previews of your feeds: Classic (plain), ClearFeed and Podcast (with previews of the previews -- nice).
Feedburner offers so many features that an updated interface was in order, and I think they've done a great job. Look for even more improvements in the near future. This is a company that's on top of their services, and I recommend giving them a try.
For more information about the new design and interface, visit the Feedburner Weblog.