I went with 3rd-4th.

Going from the NES to Genesis and SNES was a huge leap not just in graphics, but presentation. There was more you could do with environments, effects, and more that have become standard. The music quality went up a lot and was really close to CD quality, especially the SNES. This is also the generation we went from 1 game portable systems to portable systems with interchangeable carts. It felt like console gaming on the go for the first time ever. This was also the generation that sparked "console wars" that nowadays is looked down on, but back then it was fun. This was also the generation we got ratings boards for games and got more standards for the industry.

Also this was the leap where it actually felt like you could play arcade games at home. While the SNES and Genesis did a decent job at this for most games it was the NEO GEO that really made that a reality. It showed that you can have the exact same experience at home while not having to go to an arcade. Let's not forget that this was the leap that technically made arcade sticks standard.

Speaking of arcade sticks, controllers were vastly improved in the leap also. The NES controller started the standard for what controllers should be like where the SNES perfected it. The SNES controller took what was good about the NES controller and improved on it. We went from 2 face buttons to the 4 button layout that is still used to this day. The left and right trigger buttons were also introduced making more buttons available without compromising the experience. The Genesis has 3 buttons and the super pad for that has 6, but I think we all can agree that it wasn't a good layout, and it showed when the triggers and 4 face buttons became the standard instead.

This was also the leap where we started adopting CDs into gaming. Of course it was mostly used for silly things, but this showed what CDs could do for gaming. It was the 4th-5th generation leap that really showed that CDs were better for gaming than carts. This argument can also be used as to why the 4th-5th leap was the biggest jump.

Of course every generation, or generation leap has downfalls, but I think the 3rd-4th gen leap in terms of what has become standard, improving on aspects of game design, music, creativity, and more is what led to more innovation for future generations. The 3rd generation was the spark while the 4th generation was the light that showed what was possible.

Second to third for 2D graphics
Fifth to sixth for 3D graphics

Forth to fifth was a step backwards, the 3D technology clearly wasn't there yet, and the visuals were horrible as a result.

I'm gonna go with 6th to 7th personally. 

Not only was the leap from PS2/Xbox/Gamecube graphics to the kind of visuals we ended up seeing in the likes of the Uncharted and Gears of War games absolutely gargantuan, plus the greater scale and scene complexity, but the Wii's motion controls were a quantum leap for me in terms of gameplay. Being able to aim with pinpoint precision in Metroid Prime 3 or swing a sword with my own arm in Red Steel 2/Skyward Sword/Wii Sports Resort felt like something from the future brought back in time to the present.

Every gap before 6th to 7th was enormous as well.

In terms of immediate impact, nothing comes close to the jump from 4th to 5th. Games like Ridge Racer for the PS1, Panzer Dragoon on the Saturn, and especially Mario 64 really proved what 3d gaming could do at launch and showed why the new systems were huge upgrades over the older systems.

5th to 6th also had a pretty big immediate impact. The Dreamcast launched with Sonic Adventure and Soul Caliber which were mind-blowing for the late 90s. The Xbox launched with Halo. And the Gamecube launched with Rogue Leader and very soon afterwards had Melee. The PS2 not so much though.

When it comes to the 7th gen I feel it took a while for the systems to show that kind of impact. The 360 was out for a year by the time Gears of War launched, the same for the PS3 with Uncharted, The launch games for both systems were not that impressive graphically. I kind of feel the same for the jump from the Atari 2600 to the NES. By the time the NES launched in America its games were a huge leap over the 2600, but when it launched as the Famicom in Japan in 1983 it didn't have revolutionary games like Super Mario Bros. yet.

I am going against the grain and say the jump to the PS2/XB/GC was comparable with installing a Voodoo 3D accelerator card on your PC. 3D graphics went from low res 320p trash to playable 480p 60fps smoothness (on some games lime Metroid Prime). Dual analog controls became standard in that gen as well and 16:9 support. 16bit did have 3D, remember Star Fox et al, not a novelty of PS1/N64?

SNES/Genesis games are very playable today and so is anything on PS2 and beyond but PS1/N64 gen games are barely playable on real hardware.

I agree to an extent, going from PS1/N64 to PS2/Gamecube was a massive leap and the SNES gen did indeed have a few polygonal games.

As far as PS1/N64 games not being playable on the actual hardware though, I think that really depends on the game; I'd never want to play Banjo Tooie or Conker's Bad Fur Day on an actual 64 again, the framerate would give me a stroke, but I think games like Starfox 64 and F-Zero X hold up well.

Fourth to fifth: 3D graphics and 32bit CPUs (some even 64bit internally, although the address bus was narrower), opening new possibilities and filling the gap with PCs (if not in performances, at least in theoretical capabilities)

The SNES/Mega Drive actually could render 3d polygonal worlds just like the PS1/N64 and Saturn.

In-fact one great example of this is StarFox 2 on the Super Nintendo... Which could even texture 3D polygonal surfaces.
https://www.nintendolife.com/reviews/snes/star_fox_2


Now it's not the SNES doing that natively of course, but a chip inside the cartridge (FX 2) that is doing all the heavy lifting, could be argued that a more powerful chip could have brought even more impressive visuals.

The jump from the SNES to the N64 when comparing native base hardware is definitely the largest jump.
The SNES had 256kb of total ram (System+Audio+Video) and the Nintendo 64 had 4,194,304kb of total ram, which could also be doubled.

SNES had a 1.5MIPS CPU, N64 was 125MIPS. (Millions of Instructions Per Second.)


Says it all really.

I agree that Donkey Kong is terrible on the 2600.  Mario is pretty good (relative to SMB).  Anyway, I don't disagree with you that NES is when we started to see faces (though they were still not very good).  But, the fact remains that those characters were created and appeared on systems prior to gen 3.  The fact that they made the generational leap, and Mario was spun off into his own series, is evidence that they were already "memorable characters", at least to some degree, before appearing on the NES.  Definitely Pacman was memorable prior to the NES.  

The Donkey Kong character really sucks on the 2600 though.  Like, bigtime.  Could be the worst looking character in the history of gaming.  

SNES to N64. There is no other answer.