Your post didn't have a lot of info to really reply with any real insight. I have found that both methods can work depending on the situation. Unfortunately, dating can be almost a sport at times and everyone is different. So different tactics, work on different people.

I would remain friends if it is within reason to do so. Like if you guys are in the same circle of friends, or she lives close by or so on. But I would not go out of my way to keep in contact with her by any means. Like EnglishLad said, you might only be torturing yourself by doing that and dragging the inevitable out for a long time. My thought process always was that if there is a physical and emotional attraction than it will almost happen for a couple without either of them really trying. And if you have to try and go through a ton of effort just to impress a woman/girl to date you ... is she really worth that aggravation??? I believe that strong relationships are ones where you love and accept one another for who you are and not how much you do to impress somebody.

Good Luck!!!