I think the one major point that stands out, at least in the story elements between the two, is that Crono Trigger is taking characters who chose to act upon their environment, whereas Cross is the environment acting upon the characters. Active vs passive story telling. While either can be used for its particular advantages, active is usually more compelling, and it doesn't help that while Cross is a passive story, its attempted to be disguised as an active one by making it unnecessarily convoluted.
Any particular tie Cross has to Trigger is part of this guise to try to make it 'active', which the story isn't. Had Cross ditched the 'chrono' attachment and kept to its strengths in passive story play, then it would be a game worth its review ratings.
In regards to the music, while I will say some soundtracks are pretty neat on Cross, those generally get washed out (unless the person knows to listen for them) because they don't really connect as well with the pacing of the story to make a fluid tie, and even the few moments that do have that, are forgotten against the constant drone of the stupid combat music.
