In the US, capital punishment has to be based off of scientific evidence towards reliability at causing cardiac arrest within an expected time-period-- likely also an expedient cessation of brainstem functions.

A bullet to the head can mean everything or nothing. If a bullet doesn't hit the softer parts of your temple, the centre 20% of the brain, or the area of brain between the occiput and the mandible, there's a fair chance of a survival or a slow death.

If I were ever to be executed I'd want it to be from decapitation. There's limited evidence that the head can maintain consciousness for a few seconds but that's preferable to being tied down and having poison injected into you.