Introvert and extrovert (guys) like the same (shy) girl. His niceness is getting in my way all the time?

Basically the situation is quite messy. There is me, a good guy friend and a girl we both like.

I've liked this girl for several months now, but she had a boyfriend with whom she recently broke up with (like a month ago). She is incredibly shy. I mean I don't care if I have to initiate EVERYTHING but sometimes it would be nice if she did. However, I don't expect that much since she "just" broke up with her bf.
I'm the only guy who knows she is single because a friend of her told me.
All of her female friends (who are not shy at all) think that we would fit together quite well and really want me to get together with her.

The problem: a guy friend of mine who happens to live with me and other guy friends. He's extremely introverted, ALWAYS nice and hasn't ever had a gf.

I mean, he is a good friend of mine and I don't mean to be rude but I can say with great confidence that I'm way better looking than him. I know this sounds very superficial but that's just how it is (of course I haven't told him that). Sometimes I have the feeling that he is always nice because otherwise nobody would like him which I find total bs because some people take advantage of him. Sometimes I feel like I need to take care of him and I told him that he should stop being THAT nice due to people taking advantage of him but in that aspect he is very ignorant and doesn't want to hear the truth.

Anyway, some weeks ago I learned from another guy friend that he likes her as well (and he has from the start) but never told me. So I asked him and he nervously told me it was true.

The girls and us guys do lots of stuff together but he desperately tries to get her to like him by being nice all the time which pisses me off. Her best friend assured me that my crush only sees him as a friend.

Is there any chance she prefers a passive nice guy? I'm nice as well but I feel like he is trying too hard.
Anyone have any advice how to act?
Introvert and extrovert (guys) like the same (shy) girl. His niceness is getting in my way all the time?
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