Wirelessly posted (BlackBerry8530/5.0.0.601 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
AA miles would be better for all of these trips. If you were willing to fly to Lima or Bolivia on AA (and then get to CUZ on a separate ticket), you could use BA miles economically for the AA flights.
On trips to Europe, Asia, and Australia, you will pay hefty fuel surcharges if you redeem BA miles.