We fly BA to New York this year, and were happily surprised with how tasty the food was (and we were in economy). They took part in some major research a couple of years back (Heston whatshisface was involved), and have been upgrading the food as a result.
Both our evening meal, and sandwich on the way out, and our cooked breakfast on the way home, were beautiful. They had lots of different parts to it (hot meal was honey and mustard chicken, plus a pot of couscous and veg, a nice bread roll and butter, and a yummy chocolate mousse). If your kids are happy with whatever comes their way at home, I'm sure they'll be fine with the adult meals!