Here's the deal- it's not really one or the other all the time. Honestly, no girl wants an entirely submissive guy, but it's more of a continuum rather than just black or white. Some guys are very dominant in all aspects of their lives (must be on the upper end of the power dynamic in a relationship, must be the leader, must make decisions,must make the first move) and therefore want girls who are willing to be more submissive. Some guys are very submissive (tend to let others make all the decisions, let others make the move, don't have upper hand in the power dynamic) so they want a girl who is more dominant. But most guys fall somewhere in between, as do most girls. I personally don't mind making the first move if I really like a guy and just because he doesn't make a move doesn't make him unattractive, nor does it make him entirely submissive. Lots of guys are shy at first but once you get to know them in a relationship they assert themselves quite a bit.
Basically, it's a personal preference amongst girls,as it is with guys. What you need is to find a girl who compliments you on the spectrum of dominance, if you're in the low end of the middle (which it kind of sounds like to me), you need a girl in the high end of the middle.