It really only matters if they are not used to handling. If they have to be loaded with an electric prod into a trailer, and are stressed and freaked all the way to the processor, then put down in the trailer or a shoot, etc, as you can see, not so humane and lots of stress hormones coursing through the muscles! MOST places have a field butcher that comes out to the property and puts down the animal and does the blood letting, eviserating (removes the inards) and skinning. Then hangs the carcass and transports it to the finish butcher who does the cutting into roasts etc etc etc. But I have seen it done the first way as well, and if the animal is used to trailering and being led then they get led on with a halter and to them it is just another ride in the trailer, no stress, just as humane and nice. (like 4h animals that trailer to some shows for judging, they have to be comfortable with the trailer and whatnot, so going to the processor would be just like going to another show up until the lights go out).
Sorry if I am grossing anyone out, I am a huge Meet your Meat person. Former vegetarian for ethical reasons, now that humane and grass fed has taken off I can find sources I like and trust. But even then, I prefer to research actual ranches and processors not just grab anything with the organic label, etc. If I don't know exactly how it was raised and butchered I ain't buying or eating it.
*Edited to add* cursury google search shows that halal has alot to do with cleanlines but also that the name of god must be spoken during slaughter, the animal has to be hung to bleed out (thats pretty much always done) but it looks like they do a throat slit. No bullet to the head, which is my preference. It does say that the instrument must be sharp to ensure humane slaugher, but unless you hit and sever the spinal cord, and be REALLY SUPERHUMAN FAST ABOUT IT, in my oppinion, a bullet is always gonna be faster and more instant. The animal also CANNOT BE UNCONCIOUS, so yeah, having your throat slit while fully awake vs a bullet to the brain. I'll take the bullet. So I may have to ask about having my own butcher come do things and see what they say.