I don't know the weights, but I can tell you the Shimano 333 has a smaller shell than the Sturmey Archer ones, so it definitely looks lighter. And the Shimano bell crank thingie is very cool as well. If I weren't such an anglophile I would have no hesitation about using a 333 hub.
Maybe you should live dangerously and try a Sturmey Archer SW hub? These also have a smaller diameter shell than the AW, and the eerie-quiet springless pawls. The gearing is slightly wider than the AW: 0.72/1.0/1.38 vs 0.75/1.0/1.33 for the AW.
Despite its dubious reputation, I built up a wheel using an SW this spring, and rode it without problems in the Lake Pepin 3-Speed Tour and well as for my daily commute to work.