It depends, which I7 specifically are we talking about? An I5 3570 is going to beat an I7 at 1.6ghz any day. We need a little more info on what we are dealing with.
Also the i3 and i5 are not older generations. They are the same generation as the i7, they are just lower end... Well the i3 is, the i5 is pretty close to the i7.