I absolutely love my USA bronze. Great looking and sounding drum all around. I hated it with the stock head and 42 strand wires though. A standard single ply like a coated Ambassador and Pure Sound 20 strand really opened up the drum and I can really hear the shell. lots of good low end, very sensitive and the side sticks are to die for.
I've never done an A/B test with the Gretsch, but the smooth bronze Supraphonic is probably my all-time favorite snare drum. It's versatile, as all Supras are, but I find the tone of the bronze shell is very full and gives the drum a blending (as opposed to cutting) quality I really like.
I’ve played both. To me the Ludwig is more airy sounding than the Gretsch with more overtones. IMO, the Gretsch hardware is better. The die cast hoops on the Gretsch focus the sound over the flanged Ludwig hoops. Not better or worse, just a different sound and feel. Both great drums...darker sounding than their chrome counterparts.