There will be minimal difference in KE but a significant difference in momentum between a light and heavy arrow shot from the same bow! Even though the difference in KE will only be a couple of Ft Lbs, a 700 grain arrow will have approximately 30% more momentum than a 350 grain arrow when shot from the same bow.

edit: LOL! Shouldn't go messing around with all this arithmetic and stuff before my 2nd cup of coffee. Had to make a correction...[8D]

Interesting note though... Say the bow you're shooting spits out your arrows with 70 ft lbs of energy. You decide you want to try and get the 350 gn arrow's momentum to match the momentum of that 700 gn arrow. You have to drive that 350 grain arrow to 430 fps and 143 ft lbs of energy to get there.