*LOL what a goof, yeah I mixed up Rey/Ren there...
It sounds like comics KK has more competence because she's been through much more extreme stuff than TV has so far. Although being a Paragon fighting the anti-monitor might outclass a mere vampire in power level, in terms of horror being alone against a vampire or cult probably has different psych impact compared to teaming up with a supersonic meta and godlike aliens to battle other aliens.
I don't see why KK taking over for Bruce as main cape is objectionable, do we know if (in either the original multiverse or the new one) if Earth-1 even has someone like a Richard like Earth-9 does? Vesper apparently mentions him going to "Robin's graduation" but it might be unclear whether that means college, high school, or even elementary school.
Presumably that's one of the later (eg Jason/Tim/Steph) since we know that pre-2013 Nightwing crossed paths with Guillermo, which would be at least 2 years prior to Batman's disappearance. Kate born in 1990 would've been 23 in 2013 and 28 in 2018 when s1 starts...
I get the impression Bruce is older in earth 9 than in earth 1. While we usually just see photos of him, when Hush adopts his facsimile he looks pretty young so those photos must not be very out of date. Earth 9 grayson's born in 1990 just like Kate and Titans starts in 2017 so he's 27, just a year younger than Kate in her debut in his own as a cop though he's probably 28 (same age) when he adopts the Nightwing persona...
Probably there's a difference in experience though, since it's not entirely clear how many years Richard served as the 1st Robin Earth-9's 2015. It seems like the Earth-1(Prime?) version of Nightwing had adopted that persona MUCH earlier than in Earth-9 though.