KiNgBrAdLeY7: Chrono Trigger and the Something of Mana... Final Fantasy is largely, totally irrelevant in front of them.

awalterj: Both are must-have games so it comes down to the order in which you want to play them.

I strongly recommend starting with FF6 because Chrono Trigger has a much more interesting battle system with double and triple combo attacks involving multiple characters and there are no random encounters so it's more sensible to progress from FF6 to Chrono Trigger than vice versa.
Chrono Trigger is a bit meh at the beginning and then gets better and better, FF6 on the other hand is captivating right off the bat. I already felt fully immersed during the intro. In terms of story and atmosphere, I give FF6 the overall edge. Chrono Trigger has more humor but FF6 had a more cohesive storyline, at the cost of player freedom but it increases immersion so it's a trade-off. FF6 also has a much more interesting villain who is certified insane. Characters are memorable in both games and Chrono Trigger has my personal favorite one (Frog), overall the character stories are more mature and believable in FF6, surprisingly so for a fantasy game with cartoony cabbage head pixelated characters.
Both games have very nice tilesets and sprites with Chrono Trigger winning in the graphics department. Music is of equal top quality in both games. Definitely don't miss out on either one but for aforementioned reasons I'd say start with FF6.

pimpmonkey2382.313: FF6 is captivating at the start but gets more meh the later you get.

awalterj: It's mainly the dull combat system with all the random encounters in FF6 that is responsible for the increasing meh factor but there are enough memorable parts that keep you entertained like the Phantom Train or the Opera scene, and of course the epic finale. FF4 and FF7 have the same problem where there is some major slack during parts where you fight through a lengthy series of boring random encounters with standard mobs that require zero tactical effort to beat but all 3 games have storylines to compensate for that slack, and FF6 has perhaps the best story of the entire series. Chrono Trigger kept my interest up more consistently with far less slack and the different timelines keep things fresh in terms of the setting but imho it had less story immersion and fewer memorable high points than FF6.

pimpmonkey2382.313: Just seemed the writing and plot quality dropped off quite a bit in the last half of the game, the phantom train, etc were still first half if I remember right. After everythings destroyed most of the plot becomes NES JRPG simple.

awalterj: Hey wait, you just spoilered the end of the world, usually only religious sects can do that!

**spoiler alert**

But it is true, the end of the world can be a somewhat fun-decreasing or possibly depressing thing. Chrono Trigger manages to work around that same problem with the time traveling which freshens things up because you can travel back to the medieval ages right after witnessing the bleak future. In FF6, I thought it was cool when the whole party gets scattered around the world and you slowly reunite the party for the big showdown.

**spoiler end**