I'm sure there's a difference between picking righty and lefty, though I don't know from my own experience, as I'm a righty. A fair number of lefty musicians have learned to pick righty and you wouldn't even know who they are, as almost everyone picks righty. I am pretty certain that lefties just get used to it and can get as good as their practicing allows (that's the main factor). My Hot Rize buddy Tim O'Brien writes and throws left-handed, and has a great right hand on mandolin, fiddle, etc. That's just one example. I have seen just one pro banjo player pick lefty -- Don Lineberger, who played with Bill Monroe for about a year in the mid-60s and made a few recordings with him.
One compelling reason to pick righty is that you can use a standard instrument. That means you can borrow others' instruments when that's appropriate, and when you find a good instrument you may want to buy, you don't have to have a special neck made.
At this point in your playing, you can make the choice without having to undo any habits. I recommend the right-handed picking choice, if you can get comfortable with it.
Best of luck with both hands!