The pressure would be the same regardless of size, BUT, (I think this is how it works) the more volume you have, (ie- diameter) the more force you can apply.
Think of it like a uniform force per some unit area, applied to a piston for instance. If you have the same pressure (force/area), and two different areas (one piston bigger than other) you will have more force on the bigger one (pressure X's area).

A bigger brake line carries the same pressure, but you have the ability to apply it to more area.
While most of what you say seems logical, it's not correct when related to line size. 100 PSI at a 4 sq. in. caliper is going to provide 400 lbs of force (100 lbs/sq in x 4 sq in), whether it comes through a 1/8" line or a 2" line. The real advantage with a larger line is slightly reduced line loss due to restriction in the line, and a better pedal feel. For example, it you put a 1/64" orifice in the brake line, you would have terrible pedal feel because you'd have to overcome the resistance of pushing all that fluid through that tiny hole. Eventually, the pressure would come up to to 400 lbs, but it would take way too long, hence the bad pedal feel.

Your explanation does apply when you're talking about changing the piston size. A larger piston in the caliper would result in a proportionately higher pressure (proportional to the area, that is.)