The home console lineup has the benefit of 6 pieces of hardware. The handheld lineup only has 4 (5 if you were to count the Game Boy Color as its own thing).
I'll go home console. It's pretty telling that there are plenty of times where a home console title gets a port or remake on a handheld, but not often the other way around.

While it's one piece of hardware, and technically one generation - from a gamer standpoint, because of the sleeper hit like curve of the Gameboy, it was as though there were two generations. The first one when it launched, and had games like Mystic Quest, Metroid 2, Link's Awakening, Mario and the Six Golden Coins, Kirby's Dreamland that occurred during the late NES/early SNES... and then the Pokemon/GBC era which was a whole lot bigger than the original, and occurred largely during the N64 era.

Bit of trivia - There was this period of time when Nintendo handhelds were their primary source of revenue, despite the fact that the vast majority of their resources were dumped into the home console business, which had investors headscratching as to why they were structured that way. Then the Wii took them all by surprise, and you got that MASSIVE late-06/07/08 spike.

-------18-up readers only-------

I have always been a console gamer, but their handhelds were always near and dear to my heart. Every time one would release, I would look at it, tell myself no, and then end up buying it anyway because they were just so affordable, cool and fun to own and play. They also had great library of games (and third party support).

Their handheld line has been more consistent in terms of overall value proposition, product design and support.
That said home consoles had their mainline and most ambitious 1st party games....so I'll go with home consoles.

Personally, when I think of the greatest games Nintendo has produced, the ones that define their special brand of magic, they're nearly all home console titles; Super Mario Bros 1 & 3, Super Mario World, A Link to the Past, Yoshi's Island, the Donkey Kong Country games, Ocarina of Time, Mario 64, Metroid Prime, Mario Galaxy 1 & 2, Xenoblade Chronicles, Breath of the Wild, Mario Odyssey.

With a lineup like that, I simply have to give my vote to the consoles.

The home consoles always provided the more immersive experiences just based on the realities and limitations of the portable platform. As a result, I have naturally had more great experiences and memories playing home console games than handhelds since the former is just more appealing and I want to spend more time with it (higher res, better graphics, nice big screen, etc.). That isn't to say that I didn't have some great memories my handhelds such as Pokemon gen 1 and 2, Sonic Advance, etc. It's also the reality that there were times (such as being on vacation) when I just didn't have access to a home console and so my handhelds gave me some really wonderful experiences that consoles couldn't because of the circumstances.

I'm a SNES and a 2DS owner. I have to say that I have enjoyed the home consoles better. I mean, most of my favorite games are there. And the SNES is still my favorite console.

I still love a lot of NES games, a lot of Wii games... And overall, I'm not that much of a handheld gamer.

(I love my 2DS, just to clarify)

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.

Home consoles by a country mile. Almost all timeless classics were developed for the home consoles.

I enjoyed them both, but I definitely logged more hours by far on the home consoles than with the handhelds.  With relation to that, I also use my Switch docked more often than not, but it's portability has increased the amount of time I spend gaming due to being able to continue my games at work on lunchbreak and anywhere else I go out of the house.