I disagree. Metroid Prime had the same eerie environment and exploration that the 2D Metroids had. If anything, it even improved and made the environment even more eerie. If only they brought Kraid to the Prime series. He was my favorite boss and would have been outstanding in 3d.

Grand Theft Auto.

It went from an ugly 2D looking game, into an open-ended realistic looking 3D world.

Mario, Zelda, Metroid

I'll say Mario.

I would have to say Metal Gear and GTA also. Zelda, Mario, and Metroid all rocked in 2D and then 3D but with MG and GTA it was like light and day. The 3D evolutions I think made the earlier ones unplayable. I can't say the same about the three tier Nintendo mascots because I personally still think at least by a small margin, they all played better in 2D. Out of them though, I'd probably give it up to Mario.

I think the 3-D Metroids are too linear compared to the 2-D ones.

I'm always getting some radio commands and maps telling me where to go and what to do.

On the NES I was alone and lost and wandering around in space forever.

I think that's an improvement, but... makes the 2-D and 3-D games completely different.

I think Mario made the most drastic jump without losing any of "its essence."

Yeah, Nintendo handled it better than anyone else:
Metroid, Zelda and Mario.

But, for me, Mario didn't do it as well as Metroid and Zelda. Don't get me wrong, Mario 64 was an amazing game; but when I look at it, I have more fun playing the 2D Marios than I have playing the 3D Marios; I've replayed SMB1, SMB3 and SMW countless times, Mario 64 only a handful.

I think the reason is Mario already perfected the platforming genre in the 2D era, switching to 3D was a "necessary evil" for Mario, the times required it, and Nintendo did the most of it, but the genre just works better in 2D, no matter how good Mario controls or how smart the camera is.

For Metroid and Zelda tho, the switch to 3D was a more natural evolution, which added a lot to the series and made the franchises even stronger. Adventure games that are about exploration and puzzle solving benefit from the vastness of a 3D world. Platformers are more fun when you have to get from A to B.

Other franchises that did well going from 2D to 3D:
Duke Nukem
Honestly I can't think of any other.

Mario featured the most successful transition...

Mario and Zelda

well i have to say zelda,mario and metroid,all their jumps to 3D were fantastic