They're both frozen/chilled drinks, so both have the potential for brain freeze.
Living in the official Slurpee Captial of the world (9 years straight and counting), I'm obviously going for the "slushie". I still enjoy the odd milkshake or two, but they give me massive mudbutt so I can't have them too often nor can I have them on an empty stomach.
I REALLY like slushies, but there are only some flavours I like. Plus, my ABSOLUTE fave cold drink is a chocolate banana milkshake. Therefore, milkshakes win for me.
The ones you get at McDonalds are pretty much a neat cross (if it's intentional or not i'll have no clue) between the two so i'd say that but with the abscene of such a choice i'll say milkshakes.