The Mythbusters did some expirements to try and prove/disprove this. They busted it --> the subjects were more hungover when they just drank beer and less hungover when they mixed. They rated their dehydration, headache, sensitivity to light, sensitvity to loud noise and dizzyness (spun them around in a chair until they asked for mercy of puked) and made them memorize a bunch of stuff.
The little rhyme they test was different though:
Stick to beer, you're in the clear
Beer then liquor, never sicker.