Some initial thoughts:
The widget seems to perform faster then Google's at coming up with search suggestions. I also actually like the way the search results look more than Google. You can click anywhere on the result to go to the page, rather than just the title. Seems a bit more mobile friendly.
The Bing app also has a built-in browser. The search widget seems to be the only way to access it, or through the search box at the top of the app. It seems very capable and feels very fast. Might just be placebo effect, but it might be faster at loading pages then the built in browser. It is probably using the same engine as the built in browser, so who knows.
The browser does have a "favorites" feature which I assume is like bookmarks, but I'm unable to figure out how to add something to it. Also, the search box doesn't go away as you scroll down the page - a feature that used to bother me on the default browser but I have come to like. There appears to be no way to open a result in the default browser, if you wanted its features like saving images, adding bookmarks, etc. which is a drawback.
The image search is really cool, definitely better than Google's (as was the desktop version until recently), although it seems to be mysteriously lacking the feature to save or send images or set wallpapers from the images you find. You can pretty much search and view, that's it.
Movies feature is nice. Don't know if I'd use it over Flickster. It does have all the info available on one page, which is nice, but doesn't have movie trailers and you can't search by theater, just by movie.
Maps is okay. Google Maps is just such a mature product with Latitude, layers, labs, etc. that I couldn't see myself switching to Bing maps any time soon. Another poster said it had better traffic data, but it doesn't have Navigation (just directions). Might be a sufficient alternative if for some reason Google Maps is bugging out or something.
The news section just shows headlines for articles which link to the original articles on their respective pages. The interface looks the same to the search results. Nice for some simple browsing maybe.
The last thing is the picture of the day. Today's is of some mountains in China somewhere. The image actually looks a bit crappy, like it is compressed weird or something, but that might just be today. If you dismiss the menu at the bottom of the app, you will get highlight spots where you can click and learn more about the image. A nice feature, but they have it on their home page, too, and I never use it (or Bing, for that matter).
I'll play around with it a little more to see if it sticks. Overall I'd say it's a nice initial offering from Bing, and better than the crap that usually comes out of Microsoft. Missing features like the ability to save images, open links in a full featured browser, and add favorites(?) are the biggest drawbacks.