No method of execution is humane.
Beheading, even instantaneously via guillotine operating without flaw, can leave the head alive and conscious for 5-10 seconds. Usually, shock stuns the victim until death ensures moments later, but not always. Electric chairs do not always kill on the first attempt and, even if they do, it can take the condemned many seconds to die (longer than beheading). There are also stories of malfunctions and the condemned's hair being set alight with repeated shocks. Hanging does not always snap the neck (resulting in slow strangling) and you can live as long with a broken neck and crushed wind pipe as you can having been beheaded. Lethal injection is, in theory, the best, since the first drugs administered are intended to knock the condemned out before the next set paralyze breathing (etc). However, if death is delayed due to human error or the condemned having a higher than expected drug tolerance, the effects of the first drug can wear out resulting in the condemned dying in agony.
I don't see that much difference in the amount of suffering inflicted. Executions are all barbaric.