An unspoken take-away from the above is that the AA ATW desk no longer can be counted on to live up to the reputation it's still carrying from the good old days. If you can ask for one of the experienced agents by name, you'll be well taken care of - until the rate desk gets involved. The error noted above, not being able to tell an xONEx from an award, doesn't surprise me in the least. And whatever tools those agents have for pricing ATW must be primitive - it can take days for something that often should be a few keystrokes, and the result can be ridiculously incorrect.
Unfortunately, I don't know who's better. Afaik CX doesn't have dedicated ATW people so the agent may struggle with the rule set, but my unsubstantiated guess is that their pricing is prompt and correct.