The amount of friction is not decided by the size of the pad, purely by friction coefficient of the pad and the disc. This, together with the force which with it is pressed onto the disc gives the braking force.
The advantage of a larger brakepad is that it has more material to cope with the friction-heat. Therefore a larger brakepad from the same material as a smaller one will stay cooler under braking. This is the reason that a larger brakepad can be made of a material with a better friction coefficient, because it can cope with more heat.
So a larger brakepad only brakes better when it is indeed made fro material with a better friction coefficient.
Same story for a tyre. A wider tyre does not give more grip. But because it is wider, it has a larger contactpatch, and therefore has more possibilities to get rid of its heat. Therefore a wider tire can be made softer. The softer, and wider tyre can get rid of its heat easier, thus can be made of a softer rubber that gives more grip.
So getting larger brakepads is nice, but they are only effective when made of a material with higher friction coefficient.
But dont worry, most brakepads are, so combining them with a good pair of vented discs will surely improve braking!