As others have said, 2013 was clearly the 3DS' best year.
The OG DS is harder to pin down, especially since so many of use didn't really have a DS for much of its run. The DS was also the last Nintendo system to really not have software droughts, which means it was much more consistent in its output and the years were overall closer in quality. 2005 is the year the DS really showed what it could do, so I'd say then, but it's not so easy.
I'd say the DS is the first Nintendo system to never have a drought. The only other two consoles that never seemed to be short on software releases were the Wii and Switch, which both came after.
I can't speak for the NES, because hardware was not widely available for long periods of time, and by the time it got launched there was generally already something hundreds of games available.
SNES was filled with droughts, particularly in the pre-DKC era. It was kind of "here's a bunch of launch games, then we're gonna give you a few years of nothing... Oh! but here's Secret of Mana! Perhaps you should by a Sega in the meantime while we get our shit together!"
N64 and Gamecube were even worse. They got so bad that there were months where NO games were released... and I don't mean "damn, only seeing Marvel, Disney, and toy license games this month!" I mean, NO GAMES; you could literally keep track of every single release and have an opinion on it the trickle was so low in those generations.
DS and Wii had fairly solid release schedules, the Wii got shaky in its final year, but by that point it had a substantial library anyway, so it didn't feel like a drought. So Wii and DS at this point are two consoles without droughts.
Can't exactly say the same about 3DS and Wii U, but 3DS is a weird one because it's difficult to determine when we can rightly cut that generation off: for the last few years it was living on re-release fumes and its catalogue.
The Switch, on the otherhand, hasn't really had a drought yet. Last year didn't have huge first party support, but every week I found anywhere between 2-8 new games that made me think "I'd love to give that one a whirl if I had the time for it." - Essentially, Switch has had so many games that I can't even keep track of all the games I want to play, let alone all the games period (cough! SNES-N64-Gamecube!)
I describe myself as a little dose of toxic masculinity.