Grabbing a "one handed" weapon with 2 hands will give you more tip control (accuracy, that is why baseball batters and golfer use two hands ) and that extra control can also be better for feints and it can give you more blocking power.
But not really all that much extra hitting force.
If you are fighting your own weapon for control because it is very long or top heavy that can "waste" power that would have gone into your attack, thus supporting the misconception that using two hands gives you more power.
I am a book author and instructor of Medieval melee combat. Been doing it for over 30 years. when I was still in tournaments I was ranked in the top 1% world wide in our organization (full contact full speed ).
I have been ranked as King twice and now hold the rank of Duke as well as Knight. (my credentials: http://wiki.caid-commons.org/index.php/Patrick_Levi_Darkwrath)
Do not forget we are talking about Western Medieval Combat, Fencing Foils and Japanese Katanas are just not the same kind of combat as when your are in 60 pounds of steel armor.
See here for more information:
http://www.spookyfx.com/book/tromp.html