Sounds like this is more of a matter of opinion.
Technically, there have been separate generations for handheld gaming devices and home game consoles.
It gets a little fuzzy because while some would peg the original Gameboy as the 1st Gen in portable gaming, it was actually predated by Nintendo's own Game and Watch series of handheld video games. And even those were predated by Mattel's LED based sports game series of handheld video games.
But if the Gameboy is considered a proper 1st Gen handheld gaming device (as defined by what; swappable games?), then it actually corresponds with the NES and the rest of the 3rd Gen home video game consoles.
Regardless, both the 3DS and the NGP are "Next Gen" gaming devices. They're just not 8th Gen consoles.