Im a left handed pianist, but ive never had any trouble with it. I mean, my hands are different in that i can do some things more easily with one - e.g. my left hand is probably stronger, good for deep booming chords etc. but my right is more agile, better at trills or fast paced melodies, lighter things, (leggiero etc.) but i dont think thats because im left handed, i think it would be like that anyway - both my right hand and left hand are trained for certain things, but not because Ive deliberately trained them that way, but because over the 9 or however many years i played, alllll the pieces ive played have made them like that.
For piano i dont think it matters too much - your different hands get trained for certain techniques but i never found that one was "weaker" than the other. But maybe when you play other instruments it makes a difference - i play the accordion as well - now it has the keyboard on the right and the buttons on the left - probably its made like that because thats whats easier for most people.