As far as I know, "G" tells you nothing, you have to look at the cert.  If you look in the relevant AWS A5 spec, you'll see under "G" that in some of the tables where B3 will list required characteristics, "G" will say something like "as agreed between purchaser and supplier".

That doesn't mean that "G" is necessarily crap.  A lot of the G electrodes are developed to meet some kind of client- or industry-specific unpublished spec.  But you'll need to take the electrode cert to the engineer (or whoever specified the B3) on your project and see if they're okay with it.  You could get a start by checking it yourself against the B3 requirements; if it meets them, then you should be able to talk the Powers That Be into accepting the other electrode.

Hg