Both Vampires with a soul who wasted their first life, spend an eternity traveling around the world with a vampire lover causing torment and havoc, only to meet a slayer fall in love and now fight for good.
Without their personalities their pretty much the same person.
I can definitely see why she annoys people, though not in the scene your talking about, lol, but in general she is too in your face, she needed to dial it back a bit.
I think she's interesting cuz from what we learn of slayers and watchers, Buffy and Faith went undiscovered (well I'm presuming on Faith, but it always seemed that way) and were very independent, whereas Kendra was found and she was more submissive to her watcher, Kennedy was found but she doesn't seem submissive she seems closer in thinking to how Faith and Buffy are, which makes sense if you think of slayers as alone, they have to be like that, Faith even suggests thats why her and Buffy dont get alone, I could see why that would be true, if there was a pattern to slayers personalities.
I think the only problem with Kennedy is she didn't have enough screentime, she had what, probably had like a full season/season and a half worth of character development, of what should have been played out in the background and less in your face put into her however many episodes. It was too much, to fast.
But as a character, she makes sense to me.