I feel like this argument collapses when given any serious thought. Mainly because even without experiencing either, I'd consider drawing a warm bath and cutting your own wrists a very different experience compared to hanging upside down and somebody else cutting your throat.
I've never cut my wrists, but I have experienced substantial rapid blood loss. The injury itself wasn't at all painful, in the moment. Not until much later, waiting to heal. And the experience was actually rather peaceful, rather like methaqualone or diazepam. Except for the freakout about stopping the bleeding, anyway.
It's my understanding that proper kosher/halal slaughter is supposed to be non-traumatic. Because trauma makes the meat taste bad.