Milkshakes probably work best with some kind of creamy and/or sweet liquor. Also from reading online, vodka may not mix well with milk. (causes bad things to happen to the milk)
Uh, isn't a White Russian basically just a vodka/milk mix?
No, it contains Kahlua as well. A true White Russian uses cream rather than milk, though.
I looked into it a bit more to see what the chemistry reason for it is - apparently vodka is ethanol based, and if too much is mixed with milk the proteins will coagulate and cause the milk to curdle. Cream works better in a White Russian because it contains more fat, which prevents this reaction. This is also why cream liquors use cream.