Rogers.
Vandal likely has a damage soak and strength edge, but Cap is faster, more agile, far more skilled, and has the superior weapon in the form of the shield.
This is, of course, assuming this is Vandal as he's been portrayed for the vast majority of his appearances and not as Cain in Final Crisis.
Thousands of years of prep. If this fight WERE to happen, Vandal would have no doubt already have already known of Cap and have 50+ years of prep.
This is a guy who is ALWAYS three steps ahead of his best opponents.. Why? Because he's been around for-frickin-ever and has the time to do it.
He also has honed his own abilities for that long.
Cap is pretty frickin sweet, but no way he could trouble the entire JLA, much less nearly exterminate them more than once.
Vandal Savage wins and easily...