Some thoughts on the original series characters (and contrasting them with their use on the new series):
Lion-O and Panthro are the best, most fully realized characters of the core group. Lion-O's the audience identification character and the focus of the Hero's Journey arc; he's a boy trapped in a man's body who has to grow up in a real hurry. Panthro, meanwhile, is the seasoned vet who just kicks ass at everything he does; he's strong, he knows kung fu, and he's a technical genius.
The new series has played Lion-O pretty much the same as TOS; there's no artificial aging fuckery, but aside from that he's very much the same character, a boy trying to be a man after having his leadership role thrust on him.
Panthro...well, he's not there yet. So far he's the gruff one. His goofier portrayal in Berbils is actually a good thing; we're seeing him warm up a bit and the show's starting to hint that the Panthro we know and love is hiding somewhere beneath his harsh exterior. Old-series Panthro was quick to laugh; this one isn't yet but I'm hoping his shell will crack.
Cheetara's the next most well-rounded character, and she's the one with the most obvious superpower. Honestly I think she's most memorable for Lynne Lipton's sultry voice (which Lipton credits to direction from showrunner Lee Dannacher -- EDIT: and, later in the book, Starr's notes are quoted as suggesting she purr like Eartha Kitt), but she's always in the thick of things and feels like she belongs there.
She hasn't done much on the new series. I like the whole "Jaga's Cleric" angle, but they haven't really done anything with it since the second episode. I want to see her developed further, beyond just being part of a love triangle.
Tygra, by contrast...well, nobody ever seemed to know what the hell to do with him. What's interesting is that his best characterization is in two episodes with Jules Bass's fingerprints on them (under the pen name "Julian P Gardner"): Pumm-Ra and Trouble with Time. Pumm-Ra has that great bit where Tygra volunteers to infiltrate the Lair himself: "I am the architect of Cats' Lair. I know every turn, nook, and cranny." Unfortunately the architect angle isn't played up much in the rest of the series; he should be depicted as being as much a design adept as Panthro, but never really is beyond this one scene.
Trouble with Time has him artificially age and gives the interesting line at the end, "I was tempted to stay in until I was as young as Lion-O" -- it implies he's older, more tired, than the rest of the team. But that's only ever suggested again in Lion-O's Anointment; more on that in a minute.
Tygra also has an obvious superpower, in invisibility. But it's never really used to effect. He should be a ninja -- invisibility is for spying and for sneak attacks. We see a bit of that, but never very much, and it gets worse when the show goes all wacky and can't decide how the fuck his invisibility actually WORKS. (One episode actually flat-out says that the whip makes him invisible, and when he uses it on himself and Willa Nayda at the same time it causes bizarre results. And I'm not sure if that's the same episode that says he can only swim when he's invisible, but seriously, how the fuck does that work?)
Tygra's such a cipher that Starr had to completely make up a power for him when Lion-O faced off with each of the other Thundercats in Lion-O's Anointment. The others had clear abilities -- Panthro has Strength, Cheetara has Speed, and the Thunderkittens have Cunning. Since it's presumably too difficult to build an episode around Architecture or Invisibility, Tygra's episode gives him the ability to project illusions, which is never referred to in any episode before or after. (Hear the Roar includes a memo from Bass to Starr that makes that point; it's pretty funny.) If anything, if they'd had a more coherent approach, Tygra's invisibility should have been wrapped into the Mind Power mental projection, and maybe he should have been the one with an oracular Sixth Sense instead of Cheetara.
But instead, nobody ever really seemed to know how to play Tygra; it's no wonder they left him on Third Earth with Pumyra in the last season.
And this, of course, is one place where the new series has done a good job: I'm not crazy about the love triangle, but other than that Tygra's characterization has been great. The idea that he's the older adopted brother who's got a chip on his shoulder brings some real complexity to the role, and I want to know more about him.
Then we get to the Thunderkittens. They're largely extraneous, most of the writers didn't like them, and they exist mostly to act immature and fuck things up. Which is already Lion-O's job. Of course, the fact that they are mentally the same age as Lion-O is never acknowledged after the first episode (presumably because once you start tugging at the "artificial aging" thread the logic of the entire series starts to unravel -- even if you assume there's a reason Lion-O aged and the Kittens didn't, what about the Mutants? The New Thundercats? And so on). The only thing they brought to the table that the rest of the cast didn't was their bond as twins; when used well it gave them a unique character relationship, but when used poorly it made them redundant.
New series has improved them, partly by making them markedly younger than Lion-O and partly by making them Miyazakian street urchins. They're still the comic relief, but they make more sense this time around.
And then there's Snarf. I like Snarf. I like that he spends much of his time being whiny and irritating. He's the mother hen and the conscience and even though he'd just as soon stay at home where it's nice and safe he's as brave as any of the rest. I kinda wish they hadn't made him a mute on the new series, but on the other hand he WAS pretty damned irritating.
And do I need to say anything about the New Thundercats? Lynx-O was cool despite being a token; I liked him as the wise elder statesman who has turned his disability into an asset. The other two are basically useless and redundant.
And that's it for the Thundercats themselves. (Well, not Snarfer I guess, but fuck Snarfer.) Maybe I'll have a long rambly post about the bad guys at some later date. (Basically: Mumm-Ra's great, the Mutants serve as an interesting evil mirror to the Thundercats, and the Lunatacs have their moments, particularly Alluro, but showed some serious diminishing returns over time and there's a reason each season used them less than the previous.)