Where do I start? AA makes a big distinction between "international" and "domestic" upgrades, though their definition of "international" and "domestic" is curious. The free "space available" upgrades are mostly given on domestic services.

AA give OW Emerald level a few round trip upgrades per year, that can be used for international trips however below that FF level you need miles. You can upgrade from coach (economy) directly to business, and if you have a flexible fare it costs miles only at a similar rate to BA. If you have a deep discount ticket it costs you a co-pay plus more miles, though the co-pay is broadly equivalent to the price difference between 'T' and deep-discount economy fares on BA.

While there may be differences, all-in-all, for the vast majority of people the end results is broadly similar - some (like me) will find the BA system easier and cheaper, others will get a better deal from AA.