Without a doubt stay with AA and rack up the extra miles in doing so. The AA card will be recognised under the Oneworld scenario anyway. Five years ago I would have said the opposite.
CX are flying full so they choose to give away little in their homebase and put the pennies in the directors'bonuses instead meanwhile fending off the pilot strike threats etc. Diamond tier - No upgrade certificates, no tier achievement gifts etc. Well if you are in urgent need of a seat and are Diamond then you can get on. If you decide to go with CX Diamond then if anything you should register in USA or Canada. That way you earn bonuses that you would not earn as a HK resident, although you will be HK resident since the overseas CX offices have better competitive marketing incentives to get bums on seats.
As regards CX Diamond getting better treatment on CX flights that is hogwash. On some flights the chief pursers (now Inflight Entertainment Manager) might introduce themselves to you as a Diamond member and as Gold and other MPO members, on others
they do not bother and do not care. It's pot luck. Also be careful if you stay with CX not to go over the 120k miles that you need for renewal - if you do they will scratch the miles at the end of your membership year and set the clock at zero again so you might as well fly SQ and rack up miles with them thereafter.
CX are a good airline who do not fly into hillsides, which is why I have been MPO for 21 years, but the benefits and incentives of the top tier have been dramatically reduced, especially for homebase members.