Couple of things. There’s a big difference in opinion because there are many ways to look at this. A very basic approach would be to look at it from a flow standpoint, treat the pipe as a control volume and ignore the fact that the gases are being provided by an internal combustion engine, or turbocharger, etc…
There are several variables in a flow problem such as this, massflow, density, velocity and diameter. Massflow is provided by the motor, turbo, whatever, and doesn’t change, so the variables become density, velocity and diameter. Since flow out of the motor, turbo, whatever is pretty slow (I realize it’s NOT slow, but it’s definitely less than mach 0.3) one can assume incompressible flow and generally get away with it. So, density aint changing either, since the air is not being compressed (yes, I realize that air is being compressed, but it’s at another point, and doesn’t relate to this, it’s not being compressed at the downpipe at all) That leaves us velocity and diameter. Diameter goes up, velocity goes down. So now that we have that cleared up, lets look at things like pressure and shit, b/c I know everyone loves that. There’s two pressures to be aware of, static pressure and dynamic pressure. Together they form the total pressure. Static pressure is just what the pressure of the air is… (I know it’s ambiguous as shit, but when you see what dynamic is, it’ll make sense). Now dynamic pressure is the additional pressure that you get from all that fast moving air smacking into you. If you put them together, you get total pressure. Total pressure is constant, because you’re not changing anything at this point, it’s just air flowing through a pipe. Therefore, higher velocity, higher dynamic pressure, LOWER static pressure.
So wouldn’t that mean that you would want highest velocity possible, therefore smallest diameter? So why does the stock exhaust suck? Because of a little phenomenon called choked flow. You can kinda notice this with a straw. Put it in your mouth and blow a little… Now blow more… and more… More air is coming out. But after a certain point, no matter how hard you blow, the air coming out won’t increase. It’ll stay the same. Same with a car. At a certain point the mass flow becomes too large for the diameter of pipe and the velocity can’t go up anymore, so the pressure starts building, and building and your power sucks.
So now you know why certain exhausts are good for certain applications, but not others. When the massflow is high at higher rpms, the big exhaust will let it all flow out and make nice power, where the little exhaust will choke and you can kiss your top end goodbye. However, in the low rpms, when massflow is low, the big exhaust is lowering your exhaust velocity and costing you power.
This part isn’t all that useful:
Now for a bit on efficiency. There’s another thing that makes our lives an annoyance, and that’s called the no-slip condition, and it is due to viscosity. This means that air touching the walls of the pipe gets slowed to a stop, and air right above it gets slowed down as well, by friction between the particles. So you get a velocity distribution inside your pipe, with the highest velocity being in the midsection, and the velocity being zero at the walls. Now if you have a bigger diameter exhaust, there’s a much smaller area being affected by this, therefore less losses. This is the head loss that people talk about. There’s also other loss factors. Like bends for example, and expansions and contractions (like the one in your downpipe), this is why an exhaust will flow much better if it is all the same diameter, rather than expanding and contracting. So you gain a bit from expanding to 3" from 2.5", but you lose a bit from the expansion as well.
And now for how it relates to turbo cars… Turbocharged cars have significantly higher temperature exhaust gases, and it is that temperature that runs the turbine, however after the turbine, there’s still tons of heat left. Heat does a couple of things. It lowers the viscosity and it raises the speed of sound of the medium. Both these things make flow a hell of a lot better, and make it easier to get the air out of your exhaust with a good velocity. Also, these cars make a lot more massflow than their normally aspirated counterparts. With those specific circumstances it becomes a lot better to have that big kitten eating exhaust.