I'm on my third Nook (now the Nook HD) because I love it so much. And they are on super sale now because B&N is getting out of the tablet manufacturing business (but still supporting the e-book business). I was tempted by the Nook HD+ because of the low price, but glad I resisted. As the other poster mentioned, the larger tablets and be harder to hold to read for long periods of time. But I also have an Android tablet for more "tablet-like" functions, so I had that backup. If I didn't have it already, I probably would have gone ahead and gotten the HD+. I have a stand that I often use to hold my Nook when I'm reading and use it for my tablet sometimes, as well, so there are options. (The stand is actually a picture holder/stand I bought from Michael's and it works perfectly
)
The price of a Nook compared to an iPad is significant; even more so now. It does not, however, have the option of getting the 3G/4G service plan, as it does not have that capability -- it is WiFi only. So that's something to consider if you need that.
Anything I know about a Kindle is from reading, as I have never had, nor used, one. As far as books go, the Kindle is limited to solely books purchased from Amazon, aside from what you borrow from the public library (a function I use extensively on my Nook -- love that capability). With Nook HD and Nook HD+ it has now been opened up to the Google Play Store and, surprisingly, they have not blocked the Kindle app. I now have Amazon books on my Nook, as well as my B&N books. Nook also allows you to load purchases made from other companies, such as Kobo. You can sideload books that you get from other sources. I don't believe Kindle allows this, but I'm not 100% sure. You can read in the sun with the new Nook HD, and you can read wearing polarized sunglasses, which was not possible with the previous Nook Color.
I have not tried connecting my Nook HD to my TV, but I know they do make the specific cable for it. I do this often with my Android tablet and it's a really nice feature to be able to take advantage of for many purposes. Since you can use a microSD card with the Nook, I don't see why you would not be able to load a workout from the Workout Blender on the card and connect the device to the TV, but I'm only speculating on that based on what I know, not what I have experienced.
I would not try to talk anyone out of an iPad. Sometimes I wish I had one just because they're what the "cool kids" have, but for practicality, I much prefer the flexibility of the Android operating system, both for my reader and my tablet (and my phone, for that matter). I'm more writing this novel to point out that if price is a consideration, checking out the Nook HD/HD+ as something that might meet your needs is worth thinking about.
I'm sure others from the iOS and Kindle side of the fence will also be able to provide a lot of good information.
Can you tell I'm passionate about my geek gadgets?!
ETA: I don't believe you can use any device to create workouts from the Workout Blender. It's a program that needs to be downloaded to a computer, not an app that can be loaded onto a tablet, no matter whether it's iOS or android. That would be a good question/confirmation to post in the Workout Blender forum for Curt to answer.