I think that desperate is when you really really want a girl, but for stupid reasons like to validate your ego, or because she is your only one, and so you can't stand to be without her, and you must have her. "I would do anything for you!" But I imagine a scenario where she's thinking, "uhh, creep, leave me alone!"
Presistent is when you go after a girl, but it's not so much of a lost case, and you just go for the heck of it, maybe because you suspect that she may give in, and SCORE!! :cheer: But you just go for the fun, and you don't really care if she rejects you or something, because you have a million other chicks, or some other reason. Presistence is a good quality, I think, confident people are presistent.
And in the first scenario it means that the case is lost, and generally the girl has her opinion made up, she does not want you. In the second scenario presistency is good, it can make her change her mind, because the girl is like 50/50.
I hope I made my point, if some enlighted one has a different opinion, shoot!