Transitioning from one system to the next is a difficult business.

It's all too easy to mess it up and either let the console being replaced go out with a whimper, leading to a late gen slump, or to fail to get the new console off the ground.

Which transition do you think Nintendo has handled the best, and how so?

This one is easy. Nintendo to Super Nintendo. It's the only time they won back-to-back home console generations.

Handled looked like handheld to me lol. Probably GBA to DS. DS was strong from the beginning from what I can remember and the transition was smooth. I think it was big that they were able to naturally move away from the GameBoy brand.

NES to SNES
GBA to DS.

The only ones.

For consumers? DS to 3DS

For Nintendo, NES to SNES

N64 to GC

GB to GBA and GBA to DS were probably the best for Nintendo. Even though the GBA sold less than the GB, that is because Nintendo cut the GBA's life very short and because the GB had an incredibly long life. Had Nintendo waited at least 2 years to release the DS, the GBA probably would've been a 100 million seller, marking the only time (so far) that Nintendo would've had back to back 100 million sellers (a feat that has only been accomplished once, with the transition from PS1 to PS2). I hesitate to say NES to SNES because even though Nintendo was the market leader in both cases, their reign was threatened by SEGA and frankly, SEGA almost beat them.

NES to SNES
GB to DS
GC to Wii

When i read the title GBA -> DS was the first thing that came to mind.
But I think GC -> Wii was better. The backwards compatibility was new for Nintendo in the home-console market and it was a lot less hassle compared to how WiiU handled Wii games. Each new home console before the Wii sold worse than its predecessor.

In the handheld market backwards compatibility was always there (up until Switch that is). 3DS played DS games, DS played GBA game, GBA played GBC games GBC played GB games.The transition is more blurry.

WiiU to Switch.

They knew exactly how to capitalize on a failing system and convert it to a success. The transition was seamless. People readily accepted completely giving up on the WiiU for the Switch.