I'd probably go with SNES to N64 just because of the big move to polygonal graphics combined with having something on the level of Super Mario 64 day one. However, just comparing the system's 2D advancements over the SNES wasn't nearly as big of a jump for me as NES to SNES or N64 to Gamecube.

Every Playstation jump was substantial too until PS3 to PS4, and Saturn to Dreamcast was also huge.

It's the 2D to 3D leap, no doubt, so SNES→N64 and Genesis→Saturn. The SNES & Genesis had much prettier graphics than their 8-bit counterparts, but the games were pretty much the same type of experiences. Likewise with every console generation since the N64/PS1/Saturn generation, as we're still playing more or less the same basic types of games we have since the latter half of the 90s.

But the advent of true 3D graphics changed everything. New genres and game experiences were able to proliferate, and old genres were reinvented. Going from Super Mario World to Super Mario 64 and from Link to the Past to Ocarina of Time was a literal and figurative game-changer. First-person games were tailor-made for 3D and really blew up in the 90s, with GoldenEye 007, Turok, and Perfect Dark being among the most popular of such games on console. While even back then I personally felt that most of those 90s-era 3D games weren't all that nice to look at and that the transition was a very rough one, what the 2D-to-3D switch did to move gaming forward was obvious and cannot be overestimated.

Outside of the 2d-3d jump, N64 to Gamecube. The jump from the 64 Star Wars games to Rogue Leader and the og Smash to Melee was ridiculous, and games like Luigi's Mansion and Pikmin were no slouches either. Most generations, it takes around a year for games to start coming out that really demonstrate just how much better the new console's games can look than last gen, but with the Gamecube it was clear at launch well before games like Metroid Prime or REmake came out.

Biggest: Game & Watch -> Gameboy

Also: SNES -> N64, It's not only the box, but also the controller that offered new gaming experiences.

I want to have a couple of categories to see the biggest leap forward between system to successor. And I just want to focus on the these gaming companies: Nintendo, Sega, Sony, Microsoft, Meta (as they have survived and/or surviving past the year 2000).

Hardware: PS1 to PS2. 16x times more RAM, 8.94x faster CPU Speed, 3x times more GPU clock speed.

Software graphics: 2D texture to 3D polygons. Which involves the SNES to N64 and the Genesis to Saturn.

Software support: WiiU to Switch.
WiiU had 103.6M games sold, and the Switch has, as of Dec 31, 2023, sold 1133.23M games. An increase of 10.94x times, higher than any other system-to-successor.

Controller: Sega Master to Sega Genesis.
The Master had only 6 buttons (Up, Down, Left, Right, 1, 2) and the Genesis has 12 buttons (Up, Down, Left, Right, A, B, C, X, Y, Z, Mode, Start). Yes the 6-button layout was added later into the console's life, but it became the de-facto controller.

Hardware sales: WiiU to Switch.
As of Dec 31, 2023 the Switch reached 136.26M and will continue to sell many more millions. It's predecessor, the WiiU, sold 13.56M. The Switch has sold 10.05x times more than its predecessor, higher than any other system-to-successor. 

Entertainment: Color TV Game Series to NES.
The NES, and Super Mario Bros, single-handedly saved the video game industry from extinction and proved to the world that video games can be entertaining.

Nintendo: WiiU to Switch

Sega: Master to Genesis

Sony: PS1 to PS2

Microsoft: Xbox to Xbox 360

Meta: Oculus Rift to Oculus Go

Overall: I think that Nintendo made the best leap forward from the WiiU to the Switch. The company felt the most "depressing" during the WiiU era and with the Switch era it has been given new life. I gotta give it to WiiU to Switch.

Yeah this was a massive one, we went from this

To this

Breath of the Wild and FAST Racing Neo pushed the Wii U hard, the former with stuff like its dense interactive world, volumetric lighting, physics-driven particles and realtime reflections, and the latter with fully Physically Based Rendering at 60fps alongside high quality soft shadows and motion blur.

From this

to this

The N64 was about 200 times more powerful than the SNES and 3-4 times as powerful as the PS1. Nothing else comes close to this sort of gap.

It, however, severely lacked RAM, having just about a quarter of what it reasonably should. Not to mention horribly compressed cartridge games. Talk about some of the worst design choices ever.

Does anyone care about Wii to WiiU ?
Imagine a comparison between Xenoblade 1 and Xenoblade X for example.

Oooff. Now I wanna see that !

Makes me wonder how a possible remaster/remake of Xenoblade X on a Switch successor would compare to the original too.

As great as the former look, people have too remind themselves that Monolith used a shit ton of optimization tricks to make it look like it does and stable at that with the addition of data packs.

In a new version, loadings would be quasi non-existent, popping textures(which were horrible and eyesore) would prolly be hardly seen too. They could rework physics elements and have a massive glow up to the whole thing similar to XC Definitive Edition but maybe even better.

Though I'd still like them to keep the whole "phasing through cars on the road" thing lol