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.







