I'd be beheaded by a sword, going out of my way to have such done at the Tower of London. There are three reasons for this
1) That's how Anne Boleyn was beheaded, and despite not being the best person to be married to Henry VIII, she is certainly the most famous, and her daughter went on to be Queen of England, so... -shrug-
2) This reason is much the same as why Anne did - a bit more dignified. Also, not many people are trained to do it, so it takes longer. Or at least it did in the middle ages, anyway.
3) If it wasn't already obvious, I'm just a major history geek. Though I don't much care for Anne Boleyn as much as I say her name, Jane Gray died in the same spot, and I do have respect for her.