Biggest leap forward from a system to its successor

[Shadow1980]

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.