A Link Between Worlds
I 100% complete it every single time I play through it. It is just too good.

Monster Hunter 4, but to me the 3DS was a bit of a dud overall.

Every time I played it, I just wished I was playing the same game on the Wii U instead with better graphics, a bigger screen, and more comfortable controls.

3DS had a lot great gems - my most favorite Nintendo portable (excluding the Switch that is).

I would say the game or games I enjoyed the most were....

Fire Emblem Awakening and Fates

First time getting into the series and both games are on my top 10 most played with Fates having a whopping 150+ hours (across 3 campaigns).

Just loved the story, art and overall gameplay.

Kudos to SMTIV/Apocalypse, Devil Survivors 1/2, Strange Journey and Soul Hackers as it got me into the SMT series.

Bravely Default/Second were pretty damn good and the Nintendo first party offerings like Super Mario 3D Land/Kirby Planet Robobot/Triple Deluxe, and the Zeldas were great too.

Metroid: Samus Returns. Game is brilliant and a good swang-song from Nintendo for the console.

Either way works I think. If it's only 10 I don't think you should include remakes/ports though (as amazing as the Zelda remakes are)

As for the main question my favorite is Zero Escape: Virtue's Last Reward, a very flawed masterpiece. Runners up would be Samus Returns, A Link Between Worlds and Pokémon X.

3DS is my least favorite Nintendo handheld. I actually needed to look up games released for the system to even come up with a valid choice for best game on it.
I'll go with Phoenix wright: Spirit of justice.

3DS is great. One of the better systems out there. I was one that loved the 3D effect actually, the added depth even helped. I got better at platforming for example because you can judge distances and angles better. Though on the other hand it made me worse at it on other systems without the depth, this is no joke. Anyway, my favorite games were Super Mario 3D Land, Luigi’s Mansion 2, Zelda: A Link Between Worlds, Mario Kart 7 and RE: Revelations.

I’d go with Resident Evil: Revelations as my top favorite..

Fire Emblem Fates was so good.

3DS is one of Nintendo's most underrated systems. There are at least a few contenders for the best 3DS game.
Fire Emblem: Awakening
Animal Crossing: New Leaf
Both were released in 2012 in Japan and 2013 in the rest of the world. Both changed their IP a lot as well.
If we're putting remakes in the running, then The Legend of Zelda: Ocarina of Time 3D deserves a mention.
I can scarcely pick between these three, but my heart at this exact moment says Fire Emblem: Awakening.

All these game mentions remind me what an awesome system the 3DS is with an impressive library.