No time to sleep at home or no room to sleep on board?

This is a hypothetical flylemma that could be real for me in the future and is most likely very real for potential readers in the present. What if I had to fly from NYC to Heathrow in London but because of budget restraints I could either take a flight that leaves at three in the morning or fly on a crowded plane with very limited leg room. I think I would choose the red-eye, since leg irritation can be even more aggravating than sleep deprivation, but not sure. What would you choose?