Hmm.
Well, I haven't managed to observe many greys but! I have noticed TAG's are alot more goofy and approachable (the juveniles I've interacted with came over and wanted to physically interact---and my own TAG Jacko is extremely fond of scritches and treats from *anyone* lol) and even though they will have their favourite person they are (if you socialize them of course) friendly and better (although any parrot with kids requires work and caution--lots of it) for families and multiple people households. All the CAG's I've met were more vocal but standoffish and sort of aloof. They didnt really want to be touched--except by their favourite person and someone they knew really well. They didnt even really want to vocalize in front of strangers.
I'm going to really have to head you off at the pass so to speak on cockatoos though! Those guys are cuddly and sweet yes, but also extremely loud, throw off a heavy, heavy dust (not a good idea with sensitive lungs--especially those of a baby) and they are known for being jealous to the point of violence. Their unique beak shape also means they pack the most painful and dangerous whollop behind their bite. They are also, when jealous or stressed or not getting exactly the amount of attention they demand--known for multilating themselves to the point of death, and ripping their feathers off. Google 'mytoos' and REALLY look at that site.
Then decide if you still want a cockatoo.
Btw--greys also share the tendancy to feather destruction and are highly intelligent and sensitive--needing a lot of attention as well. If you guys are really set on a bird right now I'd recommend something smaller and less complicated, like a pionus. These guys are known for being quieter, calmer and a lot more self-confident and able to amuse themselves. But really, I think that with a child that young maybe a parrot isnt such a good idea right now.