Ok, reasons WHY you need a smaller exhaust on an NA, and bigger on a turbo:
Air has mass, and thus, momentum. It requires energy to get it moving. With a smaller diameter exhaust, the velocity is increased. Due to teh increased velocity, the exhaust doesn't have time to stop moving before the next exhaust pulse exits the manifold. The momentum of the moving exhaust will help pull the exhasut along. Basically, less energy is used trying to push the exhaust through the pipes.
The downside to this is that the smaller exhaust will ultimately be a restriction on the motor at higher RPM. When you put a larger diameter exhaust on an NA, the exhaust slows down too much, or even stops moving between exhaust pulses, requiring more energy to push the exhaust out. However, in the higher RPM, it works well. So basically, the larger the exhaust, the higher up the powerband is pushed.
Turbo cars follow the SAME principals pre-turbo. Not many people understand this, but exhasut gas velocity is VERY important in spooling a turbo. If you have two manifolds, one with 3/4" runners, and one with 1" runners, the 3"4" runners will always spool faster. Ever wonder how little rotaries can push such huge turbos? Exhaust gas velocity. Now, that's not saying that a 3/4" runner won't choke off the moter higher up, it's a trade-off. Spool for ultimate power, just like swaping the exhasut housings.
Now, the turbine in a turbo spins on one principal, Pressure differential. You want the LEAST amount of restriction after a turbo to create the largest pressure difference on the two sides of the turbine. This allows the exhasut gas velocity to remain at a maximum. Ever wonder why 7Ms always boost higher with DDPs? This is why, a greater pressure differential across the turbine.
So, if your friend thinks a larger exhasut on a TURBO car will lose him power, he's dead wrong. Unless the exhasut is so fucked up that it's creating a highly turbulent flow, he can't lose power.