Well, I have flown on AA's First Class Cabin to LHR.
It is a superior product. In fact, it compares favorably to the premium products of the industry leaders in this market segment, Cathay and Singapore. (FYI, I have also flown Cathay in first class.)
From my experience, I can confirm that AA sells a great number of these seats. For AA, therefore, first class is a profitable proposition. I doubt the same was true for Continental before it decided to eliminate its first class product.
As for Business First, there isn't that much of a difference between it and AA's and UA's enhanced business class product. Both now offer the same pitch and recline as Continental does.
Furthermore, AA has improved its food service in Business. As a result of a decision to provide each and every First Class Passenger with their first choice in entrees, they now cater their Business Cabins with at least two of the entrees featured in First Class.
In light of these enhancements, Continental's BusinessFirst product is no longer that extraordinary. Since Continental introduced their BFirst product, not only has the level of business class on AA and UA improved, but so has the level of their first class. Both AA and UA now offer a "suite" seat in first class. In conjunction with those changes, AA and UA responded to their chief international competitors (i.e., BA, Cathay, etc..) by enhancing their business class products.
One of AA's main competitors BA now has a fully-flat seat in Business Class. That appears to be the next wave in business class improvements. When AA and BA begin codesharing and revenue-sharing on specific routes as part of their alliance, AA will probably upgrade its business class product so that it matches BA's, since both carriers will be marketing their flights to/from Heathrow as if they were one carrier.
Continental has yet to respond to AA and UA's improvements in their business class products. It remains to be seen whether they will be the first or last US carrier to implement a BA-type business class product. Personally, I doubt they will meet the competitive challenge, since they do not operate as many 777's as BA, AA, or UA. While one could try to cram BA's business class product into a 767, it works better within the spatial and financial envelope of a 777.