Depends what you want from a tablet. The iPad is mostly faster and is very smooth. The Kindle has better video performance - but otherwise, it is a little slower and sometimes hicks up a bit - but supposedly a new software release in the next two weeks will help with this (it's not a big deal, in my experience).
I find myself using the Kindle more than the iPad - because I have a very big book library that is much easier to read on the Kindle - you have to run through hoops to read Kindle books on the iPad through the cloud reader - so it's not that easy. Of course, I do not use the camera on the iPad. The only thing that I really wish the Kindle had that the iPad has is bluetooth - for a bluetooth keyboard, when you want to actually write more stuff on it.
I also find that the 10'' size of the iPad is not to my preference, I think it is too big for real portability but not big enough to replace a full-notebook that actually does work.
But, as I said, I mostly use the tablets for media consumption, minimal email and some gaming.
As far as applications - I love Flipboard on the iPad and Pulse on the Kindle. I think Flipboard is better overall of the two, but the difference is not that big.
FWIW - WE use the Amazon Prime on our TV for streaming movies/TV shows - so having access to the same library from the Kindle and the TV/Computers is very nice - especially when you can start on one - and it resumes from the same place on the TV/Computer.
Honestly, if you know what you want to do with the tablet - find which one has the better media/content and applications for it. But overall, I would say that the iPad is a better device, the Kindle is connected to a better service, at least for my use.