Not talking about SWU/VIP/special upgrades, the AA policy is still remarkably generous. You can upgrade on virtually any revenue ticket--except O, Q, or I-- internationally, so even with the co-pay, the total will frequently be well below the cheapest upgradeable fare on UA/DL/etc... Note that the copay goes up this week, so not as good, but still a pretty great deal.
Of course how your company accounting works with this, it may be better for you to be required to purchase a higher booking class...