Which points to use for this award?
 

I am redeeming several awards for a trip to Brazil

on AA for 200K miles
on FlyingBlue for 50K miles
on COPA for 220K miles

Balances are

Chase UR - 550K
Citi TY - 450K
AA - just short of 150K
Amex - 120K

I can redeem the AA flight on AA or on BA by transferring Chase URs
I can redeem FB flight by transferring Citi TYs or Amex MRs
I can redeem COPA flight on UA transferring Chase URs or on Singapore by transferring TYs.

which points would you use, and why?

Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)

BA Avios can only be redeemed for SAAver seats on AA metal, and BA's redemption rates govern, not AA's. Are SAAver seats currently available for the flights you want? How many Avios will BA require for the same redemption?

same 50K in AA or BA

Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)

I would probably use at least some Avios for the trip to South America, if you decide to fly on AA/LAN. You have a lot of UR points, but not so many AA miles.

Note, however, that Amex occasionally offers bonuses for converting MR points to BA Avios.

Other considerations: AAdvantage redemptions permit date and time changes without charge; BAEC charges for such changes. However, award cancellation fees for BAEC are substantially less than those for AAdvantage (unless one is an AA EXP).

Btw no fuel surcharge from Brazil so on the way back you can choose from some very interesting airlines