It can also affect many other things such as power and torque and this varies from engine to engine and vehicle to vehicle.
Generally a quality stainless steel system is a wise investment for a vehicle which is to remain with you for a long time and for various other vehicles such as 4X4's used off road and many commercial vehicles because they are obtainable cheaply and outlast steel exhausts many times, this saves considerable sums in itself and when commercials factor in lost revenue from downtime it looks even more attractive.
Stainless large bore systems do have disadvantages, generally; a larger bore exhaust may increase power slightly but this would be at the top of the rev range and you may lose some at the bottom of the rev range as these are as their name suggests, performance exhausts, this may be fine for a hard driven sports car, but for most vehicles this is a negative as they rarely use the maximum engine revs. Torque is another factor, if you gain more power you usually lose some torque and this is at the lower end of the rev range, again a heavy 4X4 relies on this torque and at the bottom end of the rev range and mid range so its not beneficial, infact its a distinct disadvantage for off road use.
In reality though, most claims for improved performance are flawed as they rely on a number of other modifications to work effectively to get the best out of the exhaust system, and in considerable testing over many years I haven't found one system which can match its claims on a rolling road, and your performance will be increased more from a drop in temperature such as winter to summer. This is because cold air is more dense than hot air entering an engine, hence intercoolers on turbocharged engines, which allows more fuel to be injected into the engine resulting in more power.