I've had good luck with BA and a boxed up bike, from Seattle to the UK and back three times. I'm hoping to use them again this spring.
The baggage rules have changed: only one checked bag is allowed these days so I'm hoping to keep extra bag fees down by putting my paniers and bar bag in a big cheap (disposable) duffel bag so I only have one extra bag.
I've worked on baggage handling systems at my local airport (SEA) and they are brutal. It's not so much careless people but the devices known as 'diverters' that shove bags from one conveyor to another that really clobber bags. Also anything a bit loose and flapping like a plastic bike bag is just asking to get caught in conveyor rollers. I don't know how they handle bikes in bags, it would be a major hassle for them to not use the conveyor system. Because of this I think it safer to box a bike with plenty of pipe foam insulation. The only problem I have had was one time when the security people opened the box, they resealed it just fine, but managed to lose my front skewer which was in the bar bag. This video is very good http://www.youtube.com/watch?v=P2jCN2nVnNY