I've been a member of both for quite a few years. The NRA, like Tom said, is the larger of the two, and the quality of their publications and mailings shows the depths of their pockets. Their magazines are slick and well designed.
GOA on the other hand has a two-color, eight page newsletter that isn't copyrighted so you can reproduce it as you like and pass it around to your friends. The information in the GOA newsletter is usually more timely than the NRA publication.
GOA also will give you voting records of the entire congress to show you how they voted on certain issues that matter to gun owners. (Like CFR and the Pickering Amendment in the last issue) GOA's grading system for political candidates is a much better indicator than the one the NRA uses. This last election, my anti-gun Republican Senator was given a 'C' by the NRA, and an 'F' by the GOA. IMO, he's never met a gun control law he didn't like.
Bottom line:
GOA is
THE "No Compromise" gun lobby.
NRA is the biggest and most powerful gun lobby.
Why choose? Join both!