Class of service matters too, since different airlines have the different multipliers. For example, AA and BA are both OneWorld carriers, so you can use the same partner airlines (CX is what I booked) for travel on either airline. The awards are not exactly the same either, but from a CX gateway (including Chicago), one way flights to Thailand are 25K on BA and 35K on AA in economy, but the miles in business class class are 50K BA v 55K AA.

Another factor to consider is whether you want to have one or more stopovers. On its one partner award, BA allows free stopover(s) in Asia before your final destination without requiring a separate award, while AA does not (on its "all partner" awards for which I noted the mileage requirements above). United allows one stopover, but I think only on a roundtrip ticket. If you plan to fly around a lot in Thailand, it may make sense to compare the RTW type tickets that allow more stops, or there are low cost carriers that you can use in Thailand, and I think there is some sort of intra-Thailand pass you can buy that offers savings if you travel enough.

The third factor to consider is fees, primarily the fuel surcharge (YQ). Flying on CX with BA miles, you would have to pay YQ, but flying CX with AA miles, you would not.

Are you comparing business (BA) to economy (CO)? BA from the US to Thailand should be 50K economy (RT), while CO is 65K. But, mileage requirements on BA could increase if you cannot do your trip completely on one carrier. Similar to a previous poster, I'm using BA miles for an award flight on CX but purchasing an inexpensive positioning flight to a gateway city (JFK) separately, and flying JFK-> HKG (stopover) -> BKK for 25K miles one way in economy. Taxes/fees on BA are much higher than AA or UA because BA charges YQ on most partner award flights.