Hanging is less reliable than one might imagine; at the time, the electric chair was touted as a humane method of execution. Really it comes down to whether you buy into the idea of the death penalty or not. by the standards of American law, the DP itself can't be considered inherently cruel and unusual (because the Constitution contemplates the possibility of the death penalty being lawfully applied in the language of the 5th amendment). So all Constitutional arguments about the DP where culpability is not in question rest upon the justice or injustice of who it can be applied to (eg not minors, because they are below the age of criminal responsibility) or how it is applied - probably the easiest line to argue, because for any given method of execution it;s relatively easy to find examples of it going gruesomely wrong and you can then argue that it would be wrong to employ a method of execution where you knew in advance of such a possibility.

Obviously I am drastically over-simplifying the legal issues here.