From what I've read, the really obvious difference is that the American Lady has 2 large "eye-spots" on the underside of the hind wing, while the Painted Lady has 4 smaller spots.
If pushed to the wall, I'd guess your photo is a Painted Lady...the black surrounding the orange on the upper wings doesn't appear as crisp as on the American Lady. The American Lady also has one white round spot in the middle outer orange blotch of the upper wing. You can see it in the link, but I don't see it in your photo.
See if you can get one to pose with its underwings showing
