If competition drives the person, who knows?

I think you should block the person and focus on yourself. You can't control others, and this person might even be dangerous.

They're trying to prove to themselves that they are better, which is a double-edged sword. When one has to go out of their way to prove this, it means that they are not convinced that they are better. They are insecure, and need constant reassurance that they are better. When a person is the better, there's no need to compare, and therefore no need to push the issue. It's pitiful, but eventually the ugliness inside shows through to the outside, it can't be helped.

It could be competitiveness, and then again, maybe she secretly admires your style... As they say, imitation is the sincerest form of flattery.

Wow you must really be great if someone wants to be just like you

Insecurity and jealously