I don't think it matters to much. To be a good piano player, you need to be good at using both of your hands. I've always been better with my dominant hand on the piano, although it's been about 8 years since I've had lessons.
Right is usually lead, left is usually chords, walks, arpeggios, etc... If you also play guitar, your right hand should be the dominant hand when you play the piano as well. My right hand can rip it on the piano due to exercising it on the guitar.
Given that most people I've known who learned piano (who are also right-handed) really struggled with left hand coordination for a while, it sounds like you've got a slight advantage. Still, it takes lots of coordination for both hands, not to mention your feet.
For an instrument played with both hands while sitting in the middle, this is actually an incredible question. I suppose if you are extremely physically lefthand biased, then you'll find it easier to play songs on the lower end of the scale- but it really requires significant abilty with both hands to play piano. And left handers usually have that ability due to the need to use the right hand to do most things in a society that makes everything righthanded. This extra practice with both hands should help, but everyone is different
I would imagine you'd need near equal strength, dexterity, etc. for both hands for piano. I don't think it'd make much of a difference...
I mean, I'm right-handed, and when I play a difficult piece on piano, or a piece where it's quite demanding on my fingers, my right hand feels stronger than my left, but it's a matter of practice at the end of the day, and the key is to use both hands in sync, rather than separately.