I own several pieces of John Walsh Walsh in vaseline/uranium opalescent, and not one of mine are marked. I do have a later piece (1930's) that is not opalescent, and it has a faint etch mark on the bottom. I don't think the early stuff was marked for the most part. I have seen photos of a couple of pieces that had an original factory Rd. number hand-scribed on the underside of the piece. They are ultra-rare though.
I agree with the other posting......If I had only Powell or JWW to choose from, I would go with JWW, but there are lots and lots of other makers who also made patterned vaseline opalescent blown ware. (p.s. I like this vase a lot!)
Mr. Vaseline Glass