Which generational leap do you think was the biggest showed the biggest gains from one gen to the next, and why?

Probably the jump from 2D to 3D graphics. Most generational jumps are pretty much different degrees of improvement over what the previous machine could do. The SNES/Mega Drive literally couldn't do what the N64/PS1/Saturn could.

Probably 8bit to 16bit. I always found that the switch from 2d to 3d was a graphical step backwards that took two generations to recover....

Probably 2nd to 3rd. Just look at Atari 2600 games compared to the NES and Master System.

Either 4th-5th gen or 5th-6th gen. N64 delivered a gigantic jump compared to Genesis/Snes, 3D gaming was kinda ugly but sure impressive. Still... damn, when you compared some of the most advanced games of 5th gen and things from Og Xbox ( like comparing Goldeneye vs Halo 2 ) you can see a gigantic gap of Gen 5th vs Gen 6th, another exemple, GTA 2 PS1 vs GTA San Andreas PS2.

4 -> 5.
Hard to deny that jump from 2D to 3D was phenomenal for it's time. Not only in terms of graphics, but it brought so many possibilities in terms of gameplay as well.

4th to 5th and then 5th to 6th in a close second. Original Xbox was able to do 1080i as well. So 360 was not the beginning of the HD era really.

I don't need to demonstrate 4th to 5th but 5th to 6th was still massive.

FF8 released the same year as Shenmue. 1999 It used pre-rendered backgrounds,had pixelated faces. Warping textures.

Shenmue was in real-time. Had lip-sync and physics. Individual fingers on hands. Manipulate objects in the wall or a table. So this is early 6th gen and late 5th gen which even then shows a massive leap. Not even fair to compare late 6th gen visuals tho.

By far the biggest leap was from the SNES to the N64.

It is easily gen 2 to gen 3.  The following things were started in generation 3:

Music in games became the norm.
Graphics good enough that you could, for the first time, create lasting characters (Mario, Link, the DQ monsters, etc...).
Light gun games became available.
The D-pad replaced the joystick.
The most popular games were made for the home instead of being arcade ports.
Games could save your progress for the first time.
The first 20+ hour RPG type games.
The introduction of cheats like the Game Genie and Konami Code.
The creation of many popular franchises: Mario, Zelda, Metroid, Tetris, Dragon Quest, Final Fantasy, Castlevania, Metal Gear, Mega Man, etc....

No other generation boasts anywhere near this much innovation.  In reality my first item, music becoming the norm, is a gigantic innovation just in itself.  And yet that is one of many, many innovations all taking place in just one generation.

Going to go against the grain and say Atari to NES.

The graphics themselves were a pretty big jump. But just as importantly, the NES had what could actually be considered music. And more important still, it allowed for larger games that allowed for actual progression in gameplay. I'd say going from games like Space Invaders and Pong to things like Zelda, Metroid, and Mega Man 2 is an even bigger leap than going from Super Mario World and Mega Man X to Ocarina of Time and Banjo Kazooie.