The thing is, a lot of the appeal of Nintendo's handhelds is the congregation of Nintendo's home console games. The Gameboy Advance was basically a portable SNES. The 3DS throughout its life went from having a lot of its hype centered around N64 titles, to some Gamecube ports, to even some Wii and Wii U ports.
In a lot of scenarios, a Nintendo handheld has the better, more varied, more "absolute" library. But its because a lot of those games didn't originate on those consoles, or because Nintendo can be slow at releasing bigger home console games consistently, that that is the case.
In a vacuum, however, with the entire library of all home consoles vs all handheld consoles considered, home consoles definitely win. They just have the more definitive games. Again, though, this is in a vacuum.
