They're fairly interchangeable from my perspective. I hear both a lot.
they mean broadly the same thing, å ha lyst til in my ears in slightly more polite. vil sounds a little more like dogged determination to my ears (in this context). To exaggerate slightly: Jeg har lyst til is closer to "I would like to (if she should like to, too)" and Jeg vil is closer to "I want to no matter what"