Onion juice is an ingredient in several topical hair growth lotions, possibly because during the middle ages, those experiencing hair loss were advised to grate an onion then rub the onion juice on their scalp.

Onion has a high sulphur content, this may be a reason why the vegetable is so valued for hair. Sulphur is know as the "beauty mineral." This mineral is necessary for formation of collagen and conservation of hair, skin and nails.

A study from the Department of Dermatology and Venereology, Baghdad Teaching Hospital, Iraq, tested the effectiveness of topical crude onion juice in the treatment of alopecia. The group using the onion juice had success in 73% of people tested in comparison to 13% of the group using tap water. Published in the Journal of Dermatology, June 2002. 
As far as I'm aware, it doesn't matter which type of onion you choose to use on your scalp. The sulphur makes it smell and all onions smell strongly.

Leave a comment with any questions you have and I will try to reply quickly.