My only problem is with Chrono Trigger in Dissidia, who would counter Crono? The Cosmos side s obviously Crono, but Lavos might just be a little too hard to have playable. And If Magus was chosen, why Crono? They aren't really enemies. More Frog and Magus would be the best choice, and if crono isn't in why bother. As for Chrono Cross, Serge and Lynx are perfectly fine choices. They balance each other, Serge has been shown to have a personality. He could join Zidane on a quest to be perverted and use swallows. (I believe Serge was suppose to perverted... right?)
Yeah, I do agree with you on the Chrono Cross thing. That would be one of the biggest rivalries, and that they'd have a silent guy on Cosmos's side would add for some good humor. Having Crono on as well would also add up to a good bit of the two of them being the only ones to communicate with one another without having to do charades.
As for Crono's rival... perhaps Queen Zeal? She was saturated with Lavos's power, and pretty much everyone hated her. Or (I know that he's not a particularly serious villain) maybe Slash would work on that one. They're both swordsmen, they wield katanas, one's good and the other's evil. It would indeed be an actual rivalry, not just one being the big bad and the other being the main hero.
Now, for your obligatory picture:
