AA miles on QR would be much less than UA miles on TK. UA's partner award chart got pretty ridiculous several years back. I guess it depends on how you earn your miles but if by credit card spend then AA miles are far far more advantageous.

For your Amex points, there's a great site to reference, shows you redemption levels for various transfer partners, AA nor UA are part of that list:
https://www.travelcodex.com/award-maximizer/