In the presence of an electron-rich species, why is Br2 the stronger electrophile than water? In the electrophilic addition of aqueous bromine to ethene, the first slow step involves the electron rich (pi bond) of ethene attacking the bromine molecule to form a carbocation and Br-:


And, then water will react with the carbocation to form 2-bromoethanol. But, why does bromine react with ethene first and not water(which is of higher concentration)? 

I think it's because Br2 is the stronger electrophile than water. But why is that? Oxygen is much more electronegative which makes H more electron deficient than Br and thus a stronger electrophile?
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.