I have neither of these birds, so I'm just telling you what I remember from my research when I first decided to get a bird of my own.
Goffins, like all cockatoos, require a lot of your attention and time. Cockatoos are very needy birds. They're also generally very mechanically adept and good at learning how to open their own cages. So a cage that has pretty foolproof closing mechanisms would be a good idea. They really, really need foraging toys that they can spend their time taking apart.
African Greys are more.. sensitive? And extremely prone to becoming one person birds. That is, a bird who only wants the attention of ONE person, and everyone else is dirt. They also need a lot of attention and cuddling, but I believe they are not necessarily very -snuggly-.
Like, a cockatoo will want you to be scritching it and such all the time, whereas the grey just wants to be with you. Not necessarily touched all the time.
Greys will need puzzle toys and plenty to keep their brains active.
Nearly all birds require the same diet, with some exceptions. Pellets, fresh fruits and vegetables (daily), limited seeds and treats, etc -- will suffice for both of these species.
Honestly, I don't think either greys or any of the cockatoos are really considered "easy birds". I would do a lot more research before even thinking about getting one.
