Thanks for the reply EvilDoctorK
I'm looking at KLM because they were significantly cheaper for business class than any of the rest. Yet, when I go into the detail of the flights (on KLM's website), I found that the flights are often on other airlines - including NWA as Soy mentioned but also Air France via Paris. I find the whole thing a bit odd to be honest.
I'm plannning a trip to LA and, given its duration, feel a business class trip would be more necessary and justified for this journey than, say, New York.
Grateful for any opinions.