In the presence of an electron-rich species, why is Br2 the stronger electrophile than water?
Short answer: you are correct that oxygen is more electronegative than bromine, but the oxygen's thirst for electrons is fairly well satisfied by 2 hydrogens, whereas the bromine -- aack! -- is attached to another electron-hungry bromine. 

Bromine will snap up electrons from moderately active metals (even from water!), but water doesn't (or else does it much more slowly). Consider iron, zinc, magnesium - all react more rapidly with bromine than with water.