First off, some of you reading this are already thinking there is an error in the title. It really should be Kindle Fire versus OTHER
Android tablets. That's because the Amazon Kindle Fire IS an Android tablet. Well, it is and it's not. It's running a customized version of Android 2.3, so yes it is android, but don't expect it to support all the android features out of the box. Amazon has excluded some features, like the Android Marketplace, choosing their own Amazon App Store in it's place. Still, it is expected that hackers will find ways to restore most if not all the open android features and apps that people want.
Amazon has done a lot to tie the Kindle Fire to their services, like digital books, MP3 downloads, download and stream movies, and as mentioned before the Amazon App Store. It also has Cloud Storage that augment the small amount of memory on the device. The digital content that you buy from Amazon doesn't need to consume precious memory (it only has 8GB compared to 16GB+ that other tablets have), as long as you can deal with the delay in transferring. With a fast network, books, songs, and other small files, it shouldn't be an issue. Large content like movies may be a challenge at times.
The closest comparison to the Kindle Fire is probably the BN Color Nook. As things stand, as long as you don't mind the closer tie in to the Amazon ecosystem, the Fire meets or beats the Nook on price and nearly every feature. Dual vs single processor, more apps, smaller, thinner, lighter, are all on the Fire side. The one small win for the Nook is the microSD slot to expand memory, but the Fire depends on the cloud for that. I expect the price of the Nook will soon drop to somewhat less than the Fire in the coming months.
If you're still sitting on the fence, and you care about browsing, the Amazon Silk browser promises to be much faster and might sway you towards the Fire. Based on a "split browser" architecture, where much of the processing is done in the cloud, relieves the tablet of some heavy lifting. In my view, this is probably the most important difference between the Kindle Fire and the other tablets. Other tablets will match or exceed some specifications, but if the browsing experience promised by Silk is really better, it will be the deciding factor for some people looking mainly at browsing as a killer app, others thinking about buying a tablet, or deciding on which of the many tablets to get. I think a lot is riding on the new browser, and I'm hopeful it will deliver.
You may also find my other article on the Fire vs iPad 2
of interest. Full specs of the Fire are there as well.