I can't say much about Breath of the Wild yet, but I can confirm that it is very much a Zelda game, though it doesn't look like anything you've seen before. Notably, it also performed a lot better than it did at preview events, where I noticed stuttering and occasional slowdown while it was connected to the dock. I wasn't expecting much from the Switch's graphical capabilities, but there are plenty of moments where Breath of the Wild is just strikingly beautiful.
The game worked equally well in TV and portable modes, and I never had any issues switching between them.