It sounds like she admires your taste a great deal.
I would just accept it as flattery!
It's not like you are trying to "compete".
There is also the possibility that she has no "best friend" and would love it if you would allow her to be closer to you. Subconsciously she may be thinking if she has the same "taste" as you then you will view her as a potential close friend.
Some people do this with their older siblings as well.
"Imitation is the sincerest form of flattery."
I wouldn't let it annoy me. The only way it would be annoying is if (you simply dislike this woman) who only wants to be like (you).
My guess is she'd love to spend some one on one time with you going shopping and meeting for coffee. She wants to be your friend!
It's impossible to have too many friends!