Now that the Switch is out I'd say hybrids!
Always preferred home consoles to play local multiplayer and handhelds to play alone, so they are both equal to me, performing different jobs.

Home consoles. Playing on a handheld isn't comfortable and not as immersive. Sound is also pretty poor from handhelds.

Consoles, all the way. Even when I played handhelds extensively as a little kid their limitations continually pissed me off.

Handhelds, by default.
I say "by default" because I don't really have a choice - even now, I find myself with most of my spare time spent away from home (and by extension, a TV I can use freely).

Handhelds. I hate playing with just a controller in my hands and a tv in the distance where I have to look at.
Splatoon was my favorite Wii U game, but I didn't play it nearly as much as other games like Mario Kart or Super Smash Brawl, because it wasn't playable on the Gamepad.
The Switch will very likely become my favorite console ever, because it can be played 100% as a handheld.

Both

Home consoles all the way. The experience on a home console is just so much more immersive than handheld whereas the only benefit of a handheld is just playing on the go as intended.

Handhelds. As I work I spend to much time commuting and I am also often outside from my home. So handhelds come in good, to catch my playtime. Switch is even better, as I can go on on big screen, when I reach home.

Handheld tv  or to a less extend handheld dvd player!

Pfff...

Battery life.