Fighting with a friend over a guy really is no fun. Letting her have him may leave you resentful and heartbroken, and her letting you have him could leave her angry at you. Losing a friend over a relationship is rarely ever worth it. In this case, if you wish to keep your friendship with this girl, it may be best to let the guy walk for both of you. However, that is much easier said than done.
In any case, either of you attempting to date this guy will no doubt harm your friendship, as I have seen it do (and have had it done to me!) many many times. Personally, I've always had an ex be off-limits for any of my friends, generally even if I don't care for the guy romantically.
Just because you dated a guy in the past doesn't mean that you still have ownership over him. If he decides not to date you that doesn't necessarily mean that your friend should be banished to not going after the love of her life or something of the sort. Would sitting down with your friend and both of you maturely discussing your feelings be of help? This scenario can't easily be answered by asking if you should "let her have him", and I'm sure that you realize that. Love can be quite hard sometimes, as can friendship, and when they mingle together, wow! Watch out!