It is a hybrid in general, but a handheld at its core. For multiplat games, the big draw to get them is the portability. If not for that, there would be no reason if you owned the other consoles. For that reason, and due to the fact that it is streamlined just like any other handheld, I will always see it as a handheld that you can play as a console. Sure you can use it on the TV when the time is available, but the main purpose of the system is to play on the go.
Now some might use it as Nintendo's next big console for Nintendo games, in which case they never use portable mode and only buy exclusives. Heck some people might have it as their only current gen gaming machine and buy third party games on it as well. In this sense, it would be a console. These people are the vast minority however.
So to reiterate, it is a hybrid by design, but a handheld at its core.