The Kindle on offer is last year's not the newest one. On some specs it is better than the Hudl, on others it isn't.
Then main advantages to the Hudl are that it is very close to the original Android as designed by Google, you have access to all the Google apps and the Play store, and it has a microSD slot, so you can add more storage if you need it. It comes with the Tesco Blinkbox film-streaming service already installed, but if you don't want to use that, it will happily use Play Movies or Netflix if you prefer.
The Kindle has been changed a lot by Amazon so that the software isn't really recognisable as Android, it is very much a different thing. You don't have access to the Google Play store generally, so you use the Amazon App store for all your purchases. This has most of the major games but I'd always recommend checking if there is a specific game or app you know will be wanted. It also uses LoveFilm for film streaming, and I am not sure if you can put Netflix on it or not.
Buildwise, I think the Kindle is probably slightly better quality than the Hudl, but there's nothing wrong with the Hudl, it's just a little chunkier and a bit less refined.
You might also want to look at the Samsung Galaxy Tab 3, which has a £20 cashback offer via PC World at the moment, making it the same price as the Hudl, that's my top choice in this price range currently.