Food is a very personal thing I guess. Much as I like spicy food at home and in restaurants, I'd rather have 'bland' on a flight. BA's preoccupation with curry is tiresome.
I prefer a leafy type salad with dressing to the random assortment of ... well... things - swimming in some liquid that often turns up on BA flights. I'm not against most of the ingredients per se but I do find the combinations that BA manages to be rather strange and discordant. But perhaps that's what you consider flavour and variety.
I don't drink alcohol on flights much at all so the US airlines policy for charging doesn't affect me at all and I vastly prefer getting a full sized soda over having to ask for multiples of the miniatures.
I don't think either is universally better than the other. I know I've had meals on both that I've enjoyed and others that I really haven't. I guess overall I find AA food to be simpler whereas BA tries to do more stuff that just shouldn't be attempted with the limitations of a plane.