I believe that hangovers are the result of by products of the ferment.
There are aldehydes, amyl alcohol, esters, ketones, fusel alcohols (DMT), Lactic acid, and other impurities that can result from the fermentation process. I rather suspect it's got a lot to do with the kinds of sugars used and the ferment variables such as temperature and oxygen content available to the yeast.
When distilling clear spirits, it is best to use a reflux column and not a pot still exactly to eliminate those things from the final product.
The Cheap Vodkas make for worse and more hangovers and from less consumption because of the lower quality of the equipment and lesser attention paid to purity and precision which causes the impurity content to be higher.
I've made some steam beers that were most unkind to me the day after consuming.
I've never heard of anything that suggests that it's the hops that causes headaches.
However, the potential for an allergy might not be too far out there.