Yeah, larger rotor=more power, for the same brake and pads, different brakes and pads have/give different power levels. For anyone between 10 and 13 stone, with most brakes 180 or 185 front and 160 or 165 rear is a good combo giving good power and modulation without being overly aggressive at low speeds (<10 mph) or underpowered at high speeds (>20mph).
Larger rotor gives more power because of three factors, the first being greater energy dissipation due to more surface passing through the pads for a given revolution, greater leverage (the radius of the rotor and wheel spoke/rim are effectively levers which act upon the hub which both are attached to, thus having a greater or lesser effect upon each other dependant of radius length, which Dylan doesn't get despite the whole forum trying to tell him otherwise, so if he pops up, take no notice!) and greater heat dissipation due to the increased surface area, maintaining the brake within its operating temperature. The friction is a constant dependant upon the pads used and the pressure applied by the brake, it does vary in use as you vary the pressure by means of the lever blade, but for any given amount of pressure the friction remains the same.
Different fluids don't alter power, but can indirectly alter the pressure, as they boil at different temperatures, when they boil they release any air absorbed within which causes the fluid to aerate and thus can be compressed rather than transferring the pressure to the pistons. So one fluid may boil before another, thus the brake with the lower boiling fluid will lose power earlier, the design of the brake has a huge effect on this though, as some will transfer heat more or less than others, which is why some brakes 'cook' sooner than others.
As Clocky says. The other point with rotor size is that most frames & forks are only warranted for rotors of a certain diameter. As an example, my FS will take a 203 on the fork but only 160 on the rear (although I only run a 180/160 set up).