You do not have access to the same apps on Kindle tablets, since they have their own app store. Kobo and Nook use Google Play, which means that you'll be able to use most apps developed for Android devices. Does this make a difference in what you can read? As far as I can tell, Amazon does not include apps for some of their direct competitors (e.g. Kobo). On the other hand, those competitors use ePub and there appear to be a few apps on the Amazon store that supports ePubs with Adobe's DRM scheme. So you can still buy books from those vendors, but it will be slightly less convenient. In other cases, Amazon's store does include apps (e.g. Zinio). At the end of the day it's best to see if Amazon's app store includes the apps that you want prior to settling on their product.

(That said, you should be able to root a Kindle Fire and get direct access to Google Play. But that's something that you'd have to ask Fire users about.)