Ooh this is a fun question and, genuinely, I'm not sure. I'm gonna stumble through my favorites for each console and then try and pick one at the end.
GAME BOY
Really no question here. I was pretty young during the Game Boy and Game Boy color days, so I barely even remember playing too many games on it. Still, I remember my first time playing Pokemon vividly. So many memories are tied to playing this thing, where I played it, and how I talked about it to my friends and family. It's still one of the few times, thanks to the game itself and who I was at the time, I achieved a real "journey into the unknown" experience. I didn't even mind when I needed my brother to help me because it felt REAL. I love this silly game.
GBA
This game probably doesn't hold up and I DON'T CARE. My memories of it are so fond I still look back at Topsy-Turvy with magic and wonder. I always loved Yoshi, and the weird faux-3D(?) artstyle in this game really did it for me and tilting the system to affect the world felt like the most incredible phenomenon at the time.
PSP
The combat in this thing hooked me and all I wanted to do was play fights over and over again. Maybe I was crazy, but 1 on 1 fights had this sense of drama and urgency. It was all about knowing the movesets and conducting reads. Pulling stuff off felt like going straight up galaxy brain and I was constantly experimenting with different characters trying to find my perfect match.
Still bummed about how the PS4 game turned out.
Nintendo DS
One of the best literal titles in games ever and really just a masterpiece from beginning to end. There are few games so perfectly designed for the system they were on and this is easily one of them. The style, the music, the creative swings between the world and its characters-- I really love this game.
Nintendo 3DS
I really liked a lot of games on 3DS. Kid Icarus Uprising was fun, but the story didn't grab me as much as it did many others. Animal Crossing New Leaf is my favorite game in that series to date, but I wanted even more ambition than that game provided. 3D Land and A Link Between Worlds are both amazing, but I gotta give my 3DS award to the Pokemon game that got me BACK IN. I adored Sun and Moon. Between the Pokemon Ride system, Totem Pokemon, the way gyms were changed and even the designs of a lot of the new Pokemon themselves, there was a lot that stood out here that really made me fall in love with Pokemon again.
Vita
It's a toss-up between Danganronpa and Persona 4 Golden. I'll give Danganronpa the edge since Persona 4 Golden is like half a port. This was my first visual novel and it was an amazing and wild ride. Danganronpa would, in later titles, get away from what I thought made the first game so great, but I have a soft spot for the entire franchise. There was a time when this game took the place of the book I was reading before bed. I would tell my friends that I felt like I was binging my favorite tv show every night, haha!
Switch
My love for ARMS will never die.
Looking at this list, as boring as it is, I guess
Pokemon Blue wins! Persona 4 Golden and Danganronpa are right up there though.
Edit: thinking about it a bit more, P4G might be the one if that counts lol.