A DS card couldn't possibly hold all of Cross's maps and FMVs. Look at FFIVDS, they struggled to make everything fit and it's not particularly huge, plus there weren't a lot of voiced scenes and they still had problems.
Yeah, though, I'd imagine the PSP would get the remake, if only because they wouldn't have much worries about fitting the game onto the disc, plus there's plenty of room for extras that way. Also, consider that Valkyrie Profile, Star Ocean 1 & 2, and other RPGs got successfull PSP remakes, SE would likely stick with the same option.
[Chrono Cross on a homebrew'd PSP is fucking gorgeous, I might add]