Both Trigger and Cross have great music composed by Yasunori Mitsuda. Many melodies in Chrono Trigger can be found in Chrono Cross.
Both games differed in their plot - Trigger was centered on time travel, while Cross focused on multiple dimensions. I appreciated the tie-ins of the characters from both games (Glenn/Frog, Balthasar, Magus/Janus, Lucca, Scala, etc.), but the story itself was very confusing for me. I was bothered with the fact that Chrono Trigger's story involved the entire planet, while Cross was focused on a single archipelago. It seemed to me the game could have just been its own, without being tied back to Chrono Trigger.
I thought there were too many characters to manage in Chrono Cross than in Trigger. Some characters, secret or regular, just didn't seem necessary to be a part of the actual party.
It's easy for me to select Chrono Trigger over Chrono Cross any time.