Every character in Chrono Cross has an Element, one of six colors that determine their elemental alignment when dealing and taking damage. They come in pairs when it comes to effectivity, and Black is paired with White.
The Black Element characters of this game are quite unique, and that's true even when considering the other Elements contain an alien, a baby dragon, and a mermaid. When you compare them against each other, however, there's a pretty obvious pecking order - here are the characters you should be focusing on.
Mojo
Mojo is good at one thing and one thing only: having high agility. He'll evade a lot more attacks than anyone else. However, this is a pretty pointless strength to have in a game where you really want every member of your party contributing to the fight.
With his very low offensive stats and lackluster Element Grid, Mojo is the most disappointing Black Element character. Sure he's the first one you can recruit, but you simply don't encounter any White Element enemies before you can recruit a different, better character who would be more suited to tackling them. Poor Mojo.
Luccia
With Black Element characters being quite rare, finding a new one is always quite exciting. Mojo is the first you'll come across, Skelly is the reward after a lengthy side quest, and Luccia is... Luccia. She is not that good. In fact, she's pretty bad.
Her stats are bad, her techs are bad, and her bad German accent is also, you guessed it, bad. What puts her above Mojo is her great Element Grid which means she can at least make a semi-decent caster if there are no alternatives. The thing is, you are bound to have alternatives by the time you reach Luccia - especially if you have Guile, who surpasses her in most ways.
Skelly
You would think that after such a slog gathering bones to create him, Skelly would end up being a pretty good character. If so, you thought wrong. Skelly is, at his best, just fine. It's one of Chrono Cross's biggest flaws that the most interesting characters end up being a bit boring to use in battle, and Skelly is one of them.
He doesn't excel in any department, having pretty "meh" strength and magic, but his techs are fun to watch, and you might use him just to feel like you got something out of that treasure hunt.
Grobyc
Being a cyborg (look at the letters in Grobyc's name) in a fantasy RPG is already enough to make you stand out, even in a cast like Chrono Cross's, but Grobyc is also a pretty good character to have around. He's a bulky boy for sure, with high health and strength, but he's not going to be casting any useful Elements anytime soon.
However, this makes him stand out as one of the only Black Element characters who can use physical attacks well. The rest of the roster is either awful at everything or more geared towards magic. Grobyc fills his niche incredibly well and makes for a great teammate when you're not playing as Lynx.
Guile
Guile has the distinction of being one of Chrono Cross's best mages without being as frail as an autumnal leaf. While his physical damage will never be impressive, he does have a neat third-tier attack that hits all enemies at once, and his HP is actually pretty nice.
But that's not why you use Guile. You use Guile for his gigantic magic stat and his completely bonkers Element Grid that features a full column of level eight slots. Guile, given enough time, can use the most powerful Elements in the game over and over without any trouble. Sure, he will be quite the dead weight for the early hours of the game where his Element Grid is a hindrance, but after racking up a nice amount of Boss Stars, he's a great addition to any team thanks to his great stats and rare Element.
Lynx
The thing about Lynx is that when you get him, it's actually just Serge in Lynx's body. This means all the same stats and techs, but in a cool, new, furry look. Thankfully, Serge is already a fantastic character with a healthy balance between physical and magical attacks - the only thing that changes is his Element.
While Black Elements are generally less multipurpose than White Elements, Lynx will still make for a brilliant all-around caster with his stupendous Element Grid and great stats. As long as you have him, just think of him as Serge, but keep in mind his altered Element. You can't really go wrong when using him.
Harle
There is only one thing stopping Harle from being the de-facto best character in the game, and that is the fact that she will end up leaving the party before the end of the game. That said, she simply is the best Black Element character in the game, and it's for a number of reasons.
Firstly, she makes for an incredible mage thanks to her huge magic stat and stupendous Element Grid. She has a ton of early slots that makes her the best character to load up on healing and utility Elements. Secondly, her techs are awesome. Moon Shine cuts magic damage for the whole party in half, which is fantastic when up against nasty bosses, and Lunairetic is received far earlier than any other character would receive their level seven tech.
Add to that how great she is as a character, and you have yourself a winner.