“What effect the condemned person will feel from the nitrogen gas itself, no one knows,” Dr. Jeffrey Keller, president of the American College of Correctional Physicians, wrote in an email. “This has never been done before. It is an experimental procedure.”
We do, in fact, know what a person feels from nitrogen suffocation, and we know because nitrogen suffocation happens accidentally with some degree of regularity from workers that don't follow proper safety protocols.
At first you feel out of breath, but you don't feel panic from it; it's like exhaling everything in your lungs, and then breathing in solely from a helium filled balloon (which I'm guessing most people have tried). You feel slightly high and light headed because the oxygen in your bloodstream is rapidly depleted; you are hypoxic. As you take a second and third breath, your vision tunnels, and you pass out. Your body has a mechanism to detect a dangerous buildup of carbon dioxide in your blood, but since you're expelling the CO2 with every breath out, and breathing nitrogen back in, that panic response doesn't get tripped.
Nitrogen suffocation has been a preferred choice for right-to-die advocates.
We can argue about how the death penalty is applied, and whether it should exist at all (I believe it should, but is almost always inappropriate), but there's no serious argument about whether nitrogen suffocation is a good or bad way to die. The people continuously fighting against this execution are fighting the method because they've lost all their other avenues to prevent the execution; attempting to call this process 'untested'--when it's been tested by a large number of people using it to end their own lives, and tested via industrial accidents--is the only option that they have left to prevent this execution.