I have had to travel to the US and Japan for work before. I always got paid overtime for basically being asleep on a plane because the whole trip (my house to airport, two hours early, then flight, then trip to hotel) always took longer than 7.5 hours.
For each and everyone of those trips (about a dozen or so) I have flown in the day before I was actually required in the clients office, then never really did more than a 7 hour day, before getting the evening to myself, I have also had a couple of occasions where I've had to go out to do work on a Saturday, then needed to be back in the clients office on the Monday, so got the Sunday all to myself in San Fran, New York, Washington or Tokyo.
Flying back is usually (from the US at least) after being with the client in the morning, then an evening flight home - again getting paid OT to sleep on the flight home, then I always had the rest of that day off (well just be available for emails).
The only time I ever had to fly in, work, sleep, work fly out was trips to Europe.
If I ever had to do an 8-10 hour flight (plus the 4 or so hours of getting to and from airport) and then straight to a customers office it would have been point blank refused and they would have had to move my flight to a day earlier.
Edit - Oh and the only time I got business class was when I had to go to Iraq for a job and the client organised the flights.