I've read the guillotine is actually less painful than the leathel injection that is standard practice in the US states which have death penalties. That could also be bullshit, because...well it makes the death penalty sound scarier, which is what everyone wants.
That's true, as far as I'm aware. Lethal injection isn't a standardized practice across the country to begin with, and it's generally optimized to make the process look peaceful from the
outside -- above and beyond the regular fuckups in application, it commonly involves chemicals that are actually pretty fucking painful, it's just (again, when the process isn't fucked up beyond its baseline) they're also sedated/paralyzed to the point they can't outwardly react.
Lots of execution methods are less painful than US lethal injections, basically. The injections just don't look it (except, of course, when they're fucked up -- this bears repeating for the third time because it's not uncommon).
If you're going for painless, there's some form of asphyxiation used for euthanasia in parts of europe (I forget the details, but I think it involves methane or something; give a google for suicide pods, iirc) that is literally painless, on top of being quick and cheap. It's not available for use in the US mostly because the companies involved in producing it refuse to sell when the purpose for its use is state sanctioned murder. Nevermind that the gigantic fucking massive issues with US capital punishment means gassing people that have too goddamn good odds of not deserving to be there isn't exactly a good look.