I don't have either birds, but I've met Macaws, Greys, Toos, and know a LOT of people who have them from different forums.
Greys are easier to keep happy than a Macaw or a Cockatoo. The biggest problem with 'toos and macaws is that they get jealous. Most toos and macaws are rehomed because they started attacking the owner's spouse or children. Greys, on the other hand, are a bit more cautious and less likely to divebomb the person they hate. I would feel pretty confident if I acquired a Grey, as long as I kept it flighted (IMPORTANT, VERY IMPORANT lol), gave it lots of chewing and foraging toys, took it outside in a carrier or a harness and socialized it well with many people. Toos and Macaws, you do all of the above, and you could still end up with an aggressive attacking bird, though you would be lessening the chances.
I would give it time with your Galah. The most simple reason for why your bird is biting so much is that it bird doesn't want to be touched by you. Just leave it alone and give it time. Work on giving treats from outside of the cage, start target training using Michaels' taming guide:
www.trainedparrot.com/taming .... and do read
www.mytoos.com Flight is very important for a Cockatoo, it's important for all birds mind you (common sense), but with Cockatoos it's pretty much imperative to keep them happy. You don't want to deal with severe behavioural issues associated with boredom and pent up energy.