Is there any advantage to booking directly through the airline website and not an OTA?
Do you get the same 24 hour cancellation on aa.com ?
Depends on the airline. Oftentimes better cancellation policy with OTA..
2 that I know off the bat:
AA does not allow free cancellations for travel under 2 days away, while booking on Priceline would allow that.
Jetblue is similar, but their policy is not allowed within 7 days, again Priceline would allow that.