No, the disc size actually makes very little difference on it's own. The 262/282 brakes have different calipers though, 262s get a 54mm piston and the 282s get a 57mm piston. That's a fair whack more area and has a big effect on pedal travel and feel, brake force and balance.
If you kept the piston area the same, a four pot caliper offer small improvements in things like reduced weight, better feel and quicker release (less brake drag), quick pad changes and cheaper pads. On and they look awesome.
The real changes are actually very small, but what they do is give you a **** load more confidence in them, which is actually worth a lot more than a brake kit which gives you a huge gain in brake force. That just makes them hard to modulate and messes up the balance so you have less confidence in them going into corners.