I say B is the real one. Something about Liberty's face in the first one is wrong. Not GLARINGLY wrong, but wrong enough that I held my own (presumably real) 1922
Peace dollar up against the screen and my eye went "now wait just a gosh-darn minute . . . "
For the record, I THINK it's something in the proportions of the face--curve of the chin, space between eye and bridge of the nose, and the shape of the nose itself.
. . . . I just looked again before posting, and guys, I FOUND IT. B is definitely the real one. Look at the distance between "1921"and the rim. My 1922 shows a similar distance to the distance shown on coin B, but coin A is squashed right up against the rim! Further, look at the noses--coin A has almost a hook or witch's bump in the nose (go look up a picture of Alan Rickman and take a look), but Coin B and the 1922 I'm using for comparison both have a "Roman" nose--very strong, not completely straight, but definitely not with that big bump.
If you have your own
Peace dollar, hold it up to your screen and let your eyes relax so they look directly at the space below the image you're comparing to (Coin A or Coin B). All of a sudden all these teensy little "something about this isn't quite right" things you can't quite put your finger on looking at the coin head-on will jump out at you. Look back at the coin directly and your eye will be disturbed but still not quite able to pick things out concretely (e.g. there is no "Her eye is one half of one millimeter too large!" moment, unless you spot that bump in the nose).