I've been reading some GD comics recently, though I'm not all the way through them. I'm sure she's got better feats later on, but from what I've seen:
I'm gunna say Cass probably takes this one, just due to speed and body-reading, and probably being stronger. Julia is a freakin' beast in hand-to-hand, but she's probably not Cass's level (especially whatever Cass's strongest point was, I'm sure).
Julia demonstrates a "body reading" skill that sufficiently enables her to out-maneuver and throw, strike, or pin the superhumanly fast and strong werecreatures and monsters, even her daughter Brittany (who, as a werecheetah, is one of the fastest types). However, this isn't as advanced as Cass's, and is a skill any veteran fighter picks up.
Julia is also fast herself, at least comic book peak human, but I don't think she's dodging bullets, at least with the ease the Cass does. She is fast enough to evade Cheetah's strikes, but that's a combination of body-reading and speed on her part.
Julia is sufficiently strong enough to deal damage and even mortal blows to much bigger creatures, including dragons and giant humanoids, and I believe she broke through a stone wall once. I think. Maybe. She
might be in Cass's strength level, but I'm not sure.
Julia does gain the "renewing" ability, which will cure all of her wounds and refresh her stamina, though it also de-ages her some. Any other abilities, I'm not sure about; chi techniques exist in the GD universe, but I haven't seen her use any.

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