I think men are more romantics but women are just better at planning things. Also, I think women tend to be more observant and cautious in approaching relationships but men just tend to jump all in when they really like a girl.
However, arwen is right... That in the long run experiences and personalities also play a big role. Depends what you consider romantic too... Is poetry romantic for you? A creative date? Words of love? Expressions of intimacy and affection? All of that does play a role as well.
Me, personally... I do not find myself as being a romantic person but when I fall on love, I do show love and affection a lot, not just romantically.