Games that presented the biggest leap over their predecessor

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Final Fantasy 4 - Huge immersive story and fleshed out characters far beyond what Final Fantasy had before.
Final Fantasy 7 - Gigantic game compared to FF6.  Lots of content.  The pinacle of video game story telling IMO.  Also the FMV graphics were very impressive in their day.

Breath of the Wild - It's 3D Zelda with the huge open world feel of the old 2D Zeldas.  Really huge and highly polished world with unparalleled freedom.
Hyrule Warriors - Just putting Dynasty Warriors in Hyrule makes the game so much better.
Mario + Rabbids - I could never get into X-Com, but I enjoyed the hell out of Mario + Rabbids.  The world and characters are a lot more interesting.

Puyo Puyo Tetris - I wasn't really a Tetris fan until I played this version.  It takes the game to a whole new level.

Assassin's Creed 2 - I felt the first game was shipped incomplete, but it had potential.  The second game fully realized that potential.

Dark Souls - I really thought Demon Souls was great back in the day, but I went back and played it after playing Dark Souls and it just feels bland by comparison.  Dark Souls has this huge varied world to navigate and conquer and it is continuous instead of always returning to a hub world.

Civilization Revolution - All the fun of a Civilization game but streamlined so you can finish a game in a couple of hours.

Wii Sports Resort - This is so many more games and much better control than Wii Sports
Mario Kart Wii - To me Mario Kart really came into its own when it gained motion controls.

Guitar Hero 1 and Rock Band 1 - This series actually started out with the games Frequency and Amplitude, neither of which used plastic instruments.  That is why Guitar Hero was a huge leap.  I didn't come in to this series until GH3, but it should be obvious how much a leap it was to have plastic instruments.  Then Rock Band came along and took this genre to the next level by having a whole band of plastic instruments.  (GH and Rockband have different publishers, but both games were originally designed by Harmonix.)