Poker Range of Hands Math

[GTSamIAm]

You're supposed to always put a player on a range of hands and an approximate percentage that the opponent has a certain hand. So you could calculate your equity weighting the chance of each poker hand. Or you could play the opponent on each specific hand according to the percentage that he has it. In the long run, shouldn't these two choices have the same expected value? Also, if you choose the hand that has the highest expected value for you, shouldn't this be more profitable than playing his range of hands? Or what about choosing the most probable hand?