IMO, and I know there are people here who disagree with me, the best way to enjoy Chrono Cross is not to consider it as a sequel to CT, but as another game that reminds you of CT. (Kind of like sequential FF titles.) I feel the connections are weak, and it feels more like a spin-off than a continuation of the story.
I think that half of the hate that CC gets is because people go into it expecting Chrono Trigger 2, which I don't think anyone will argue it is.