[0] https://www.youtube.com/watch?v=kUfF2MTnqAw
Edit: Typo
Depending on the distance and round, not only will the prisoner not experience their own death (they won't see or even hear it coming), it's astronomically unlikely to fail. High velocity rounds will pierce through the tissue more quickly than it can physically tear, and will technically exit the body before the brain matter has begun tearing. The physics of this is fascinating, because it not only ultimately destroys significant brain tissue; the process stretches out the tissue, straining and damaging the rest of the surviving brain tissue.
Of course, this is not optimized to be clean. It's gruesome, but I don't think it's necessarily cruel. One moment they're alive, the next they're not. Blunt force is still the quickest way to induce a cessation of consciousness. If the prisoner were not aware of it happening, they would probably be at greater peace at the time of their death. This could also be done remotely so as to reduce the mental toll on the executioner.
Unfortunately, it would make an open casket unlikely. But I imagine most prisoners due to be executed experience a lot of terror in the hours, days and weeks preceding their final moments under the current system. I imagine living with that anticipation is horrifying for some.
From what I can understand through cursory research, morphine is a painless way to die, so much so that doctors use it to ease patients into death when there is an acceptable lack of available treatment. Extreme euphoria followed by unconsciousness doesn't sound like a bad way to do.
http://www.bbc.co.uk/sn/tvradio/programmes/horizon/broadband...
Hypoxia seems the most kind way. Low pressure is not needed, just a lack of oxygen (by e.g. breathing helium). I suppose it's not enough of a punishment to go out this way, as it's rather pleasant as these things go (there's no feeling of suffocation) and there can even be a mild euphoria.