Zeal was profound, deep, artistic, beautiful, and tragic. It was all written by Kato, and those qualities are all more concentrated in Chrono Cross than in Chrono Trigger. Of course, the producers were different and Kato apparently wrote himself into a "explain everything on Opassa (bad pacing)" corner. Still, Kato brought the best of the best era and characters in Chrono Trigger to Chrono Cross. Without the extra characters and with better plot pacing, it would be even better. For reference, Horii wrote the basic CT plot line, and Kato tweaked it while adding 12,000 B.C. all by himself.
So it's hard to say the developers "betrayed" Chrono Trigger unless you're talking about specific things, or Yuji Horii. For the former, CT "betrayed" RPG convention at the time with New Game +, multiple endings, double techs...and Tanaka and Kato decided to continue that ideal of innovation with Cross's element system and parallel worlds. For the latter, well, I guess that's personal preference. If you feel Kato betrayed CT fans by not maintaining Horii's sense of fun, lighthearted (but subject to creating temporal plot holes) story, well, there's plenty of that in Dragon Quest. And even then, Kato put a lot of humor into Chrono Cross, in turn augmented by Richard Honeywood's love of phonetic puns. But no, it's not your "lighthearted Goku" kind of plot-driven humor.