Another thing I like to add is that, until a full saturation attack happens we really don't know just how the AA missile performs in shutting down incoming Ashm. It seems most modern missiles do some trick maneuvers, such as flying very low at first and only pop up near the target, or even before it hit the target it is able to do large G movements before impact. So we don't know just how effective those AA missiles are at shutting down incoming Ashm.
The same can be said for the Ashm, the biggest problem as usual is to acquire targets to launch towards them, and even when it is in mid air, they can be jammed, they can be set off course by decoy launcher launching chaffs, and of course they can be shut down by CIWS or AA missiles etc...
It would really go both ways, best case scenario most of the incoming missile would be shut down, or most of the incoming missiles would hit the targets, we just don't know the answer until it happens.
But I personally think the missile barrage will win the fight, even if they can shot down most of it, but all you need is 1 to hit the mark and it will most likely disable the target to take it out of combat.