Adding to what Sloth said, just because it makes more boost doesn't mean it makes more power. Every blower housing has a maximum volume and while you can always spin the internals faster (until it chokes) to move more air you do so at the expense of generating more heat. Every compressor housing, regardless of type, has efficiency islands when you relate the mass flow, compressor velocity, and pressure ratio. A compressor housing that generates 7psi at 4000rpm with a 76% efficiency will make more power than a housing making 10psi at 5000rpm with a 60% efficiency because the amount of heat induced into the system will offset the additional increase in pressure; mass flow is what needs to be looked at, not boost pressure. Intercoolers/aftercoolers help correct this issue to a degree; you are reducing flow velocity and pressure as the air now is passed through an exchanger core to get a higher air density but at a lower pressure/velocity.
A 7psi turbo should be more efficient than a 7psi supercharger due to the amount of power required to drive the supercharger vs the exhaust driven turbo. The A/R ratio and turbine wheel diameter will determine how fast a turbo spools up and more importantly, how quickly it will run out of volume and choke out (trying to pack more air in than it can).