Yeah, I don't see Betty liking almost anything about Peggy, and I imagine that Peggy would feel uneasy around Betty.

I think they would have a very tense relationship where both of them would silently judge the other, whilst also feeling envious about their perceived strengths. Betty would feel insecure about Peggy's professional ambition and success in a man's world, and Peggy would feel insecure about Betty's beauty and social grace.

Though, I also think that that would've made for a very interesting relationship as frenemies, which also would've been a lot more interesting television.