The new version of the app, available for free here [iTunes link], makes great use of the extra screen real estate afforded by the iPad and takes advantage of both portrait and landscape modes. A few other visual niceties separate the iPad from the iPhone version, creating a slicker appearance overall and implementation on the larger device.
Although there aren't nearly as many options here in terms of actually working with your Dropbox files as in the web-based interface for example, you can both view and share items with friends via e-mail. You can also send supported file types on to other native iPad applications like Pages and Keynote.
It's essentially an iPad-optimized version of Dropbox, and considering it's only the first pass we expect to see more upgrades and functionality coming along presently as well. If you have a chance to check out the app, let us know what you think in the comments.