Well my handwriting is lousy and I'm poor at a lot of fine things but I'm not sure how much of this is down to differences in motor skills and how much is due to try to mimic right handed ways of doing things with my left hand.
Take writing for example. We are using different muscles. For horizontal movement a right hander is pulling their hand further away from the body. If I write, I am pulling my hand closer to my body.
I'm not really sure about musical instruments although I'm known to use it as an excuse (had I known there was a left handed way of playing, I would have been better) but I'm not sure and there are so many other variables including where we set our standards to compare to and the standards we may need for playing with others, etc. Let's put it this way, I'm capable enough for what I do although I'd love to be Barney McKenna...
It's also difficult to asses with others as so many left handers do play right handed and you don't always know who is what.