My criteria for a game that has “good cut scenes,” is whether I can watch it if it was a movie. The Final Fantasy series is one of the most storied video game series ever. However, the story itself can be basic. They tend to follow a predictable format. A major character will die, Princess, Cid, etc. Anyway, I found FF12 to have the most impressive story of all the Final Fantasy games.
The characters were interesting, as was the story. The graphics (at the time) were great. I loved the voice acting and the overall story arc. Someone put the cut-scenes together on YouTube and from time to time I watch the “movie.” The story “begins with the defeat of the Kingdom of Dalmasca at the hands of the powerful Archadian Empire, and subsequent occupation.” Watch it, if you have time: