In general, men have far more pressure to be confident than women do.
On the other hand, If I were to be a girl I would be a lot more relaxed in may approach because I know my earnings are not the primary source of income to my family. And husband is going to take care of it anyways.
I've met more women who would prefer a relationship with a confident man who earned less than they do than I've met women who would prefer a relationship with a less-confident man who did earn more. I mean, that's all anecdotal, but I've been both (comparatively) wealthy and unconfident, poor and confident, and wealthy and confident, and as far as I can tell, the comparative level of wealth involved has little to do with dating outcomes.
On the subject of being out-earned, with traditionally male jobs falling out of favor and traditionally female jobs rising in importance and pay, it seems that us men may not end up being the primary provider for our families[1]
this is consistent with my observation both of the lower class and the upper middle class people I know.
[1]http://www.time.com/time/business/article/0,8599,2015274,00....
Thats the key right there - women are comfortable competing, they just have a hard time picturing themselves as the alpha geek hacker that this competitive language brings to mind for many people. At least thats how I interpreted it.
Also there are studies that women tend to underestimate their skills while men tend to overestimate them which might also be relevant, see Sheryl Sandberg's commencement address:
http://www.youtube.com/watch?v=AdvXCKFNqTY