I think you have that the wrong way round. The injection is far more likely to cause intense pain and suffering due to the lack of medical professionals being involved (it's not a medical procedure). The drugs are often obtained from "dodgy" sources and so the dosage can't be determined due to the variability of the drugs. The lack of medical professionals will often mean that the injections are poorly administered (e.g. missing a vein).

I was just reading a Reddit post from a veterinarian and the protocol for euthanising animals is far better than that used for lethal injections - notably pre-meds are used to sedate the patient and prevent breathing issues and panic.

A bullet or two to the head is far more effective and reliable. The only downside to lethal shooting is that it looks too barbaric to observers.