First, for a single stop, your braking performance 99.999% determined by your tires and the pavement. If you can't lock up your front tires in a panic stop, your brake system is defective.
For repeated stops, when the brakes are already hot, the heat dissipation becomes a major factor in brake performance. Unless you are running carbon-carbon disks and pads, your brakes fade as they get hotter, eventually to the point where they barely work at all. Most people will never experience that on the street. Bigger rotors and bigger pads both improve heat dissipation. More pistons generally means you run a longer pad, which spreads heat over more pad material and dissipates heat from a larger area. One thing to keep in mind with our cars is that a lot of people build these for drag racing, drag racers run small front tires that lock up with a lot less brake power, and drag racing only has to stop once between cool-downs. Street cars generally need a lot more front braking power and heat dissipation than drag cars, and road race cars need massively more.
Another factor in play is fixed vs floating calipers. Fixed calipers (at least for automotive) have pistons on both sides, and floating have pistons on one side and rely on the caliper sliding to apply force to both sides of the rotor. There's some friction in the caliper sliding, so floating calipers don't feel quite as crisp on/off as multi-piston fixed calipers.
Finally, independent of number of pistons, the ratio of master cylinder piston surface area to the total surface area of the caliper piston(s) determines the clamping force at the caliper for a given pedal pressure. When you change calipers, this ratio may change. More caliper piston surface area means more clamping force, but longer pedal travel. More master cylinder piston surface area means less clamping force and less pedal travel. There are a bunch of calculators out there to figure out how all of these things plus your pedal ratio work together. If you get your ratios out of whack, you get mushy brakes or brakes that are hard to modulate (on/off).
You also need to keep the front/rear brake bias in mind. Most proportioning valves act like a pressure regulator--they limit the max pressure you are sending to the rear brakes. For most street driving this is fine--all you really care about is that the rears aren't locking up before the fronts. For road racing or spirited street (mountain) driving, you're going to care about how the rear is behaving in relation to the front when they aren't locked up--this is why road racers run a balance-bar setup with separate front and rear master cylinders instead of a proportioning valve. The ideal ratio of your front brake power to rear is going to depend on your suspension and how you drive (and actually each specific turn you make), but too little rear bias is better than too much. Too much rear bias will cause the rear end to get loose, which is not what most people want to happen under hard braking.
So what real matters is properly matching all of your brake components. X number pistons or Y diameter discs won't mean squat if they aren't matched to the rest of the system. Fancy pads won't fix a mushy brake pedal. Most of the performance brake vendors should be happy to help you put together a decently matched system for how you plan to use it.
