First of all, we need to get our definitions of halal and haram meat strait. Beef or mutton, or chicken etc all are halal (permissible) irrespective of how the animal was slaughtered. Pork, meat from meat -eaters, birds that hunt using their talons etc are haram (non-permissible) irrespective of how and if they were slaughtered. Islamic way of slaughter renders animal meat zabiha, which is a level up from halal. There are few condition to qualify for zabiha. The animal must be halal (permissible), faced towards kaaba, and the person slaughtering the animal must recite Bismillah, and Allah o akbar. Now that is pretty much academic and I am REALLY skeptical if butchers follow these instructions. So if you ask me, I don't think we ever get a chance to eat true zabiha except during baqar-eid when we slaughter animals by ourselves while observing all the rituals. In a nutshell, halal is not fit to consume if it is non-zabihah.
I would like to add one more thing. When slaughtering an animal following Jewish or Islamic custom, the objective is to cut the blood supply to the brain by severing the carotid arteries, and jugular veins. Once this is done swiftly, animal should feel little pain. Quicker this process, least pain animal will endure. Hence there are instructions to use a very sharp tool.
