Visually, I would probably go with N64 to GC.

But going from wobbly and jittery Saturn/PS1 to Dreamcast/PS2 was, IMO, more impactful at the time.

Ah I misunderstood the question as being generational leaps, not consoles. In that case, maybe I’d need to out some thought into it… PS1 to PS2 seems like it would bigger, but GCN really was a major step up from N64. We’re talking about going from N64 to graphics which looked modern until the PS4/XBO generation.

Ps2 era no contest, from going to ps1 to ps2 was mindblowing

In terms of the biggest leaps noticeable at console launches, the PS1 to PS2 and N64 to GameCube, as have already been mentioned.

However, in terms of the biggest leaps over the entire life of the consoles and leaps in overall game design rather than just graphics, I would argue there's actually a case to be made for the Xbox OG to 360, and the PS2 to PS3. Yes, it was the first time we really got a "cross-gen" period, which was filled with what were essentially just PS2 games in HD. However, I think PS2/GC/Xbox games stayed mechanically quite similar to games from the previous console generation, whereas the 360/PS3 generation had more the feel of a big leap forward in terms of scope and ambition for games, and more developers pushing boundaries and trying out new gameplay concepts, even if some of them (*cough*motion control*cough*) turned out to be blind alleys that were best forgotten.

Dreamcast, and it's not even close.

Are you talking about the jump from Saturn to Dreamcast? From N64/PS1 to Dreamcast? Or to the subsequent generation (GCN/XB/PS2)?

I think it has to be PS1 to PS2.

Finally being able to have human emotion on characters, properly depict clothes and have fully realised 3D environments with scope and detail

To be honest I wasn't that impressed with the PS2 or GCN because the Dreamcast basically did a lot of the same things earlier, seeing Soul Calibur on the Dreamcast was more mind blowing than any PS2 or GCN title ... but I was too hard on the GCN too.

Like I remember getting a PS2 in Oct 2000 and not being impressed by really any of the launch games because they looked similar to Dreamcast games that I was already playing or in some cases worse. 

With GameCube, launch games like Star Wars: Rogue Squadron, Wave Race: Blue Storm were incredible looking for their time, I just didn't appreciate it enough because you get caught up in internet nonsense.

Now looking back on it, I realize GameCube was incredible hardware for its time, many games still look good to this day (Star Fox Adventures, Rogue Squadron II/III, Resident Evil 4, etc. etc.). I was watching some Star Fox rumors video on Youtube the other day and they showed gameplay of Star Fox Adventures and I was like "daaaamn ... that game still looks good today". 

It would probably be PS1 to PS2 or N64 to GCN.
Even if a lot of the models have looked crude for a while, it's the first generation where cartoony and realistic models look like people in 3D. The tech wasn't really there, especially for more realistic games before Dreamcast.
Switch to Switch 2 is a huge leap, Wii to Wii U was a huge leap.
The sixth generation was the first generation where 3D sandboxes and open-world became probable, though they were uncommon. Games that took 2-4 discs on PS1 were now succeeded by games that could fit on a disc. Shoot, there were even 2 PS1 games that had 5 discs. Even GameCube miniDVDs (including the few 2 disc releases) could hold so much more than N64 cartridges.

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