The 21' has much more floor space, so for dogs, I would go with it. And it has more walking and other space for you. You are one person so I suppose a 19' could work but I would not usually want to recommend one for fulltiming. I just spent a few months in the 21' and couldn't imagine, or want to do that, with the 19'. My husband was there about half of the time.
As suggested, if you have not seen both in person, you can see them in your region by visiting owners. As for backing, I don't see any difference, but I think I would have to try the 19' at the same time as a 21'. It is much easier for me to back the 21' because I had practice with the 19'! For backing, just get out and go back and look at the path the trailer is taking, then adjust the steering wheel slightly accordingly.