Is Halal Meat Generally Better Quality?
Halal meat is healthier. Research has shown that if animal has a disease it is mostly in its blood and not in the muscle. One of the compulsory point of a halal meat is that blood is fully drained from the animal. This is why it's healthier. If animal is slaughtered by electric jerk or with machine then it's. not the case most of the time.
The halal designation says nothing about the quality of meat, but whether it is licit for Muslims to consume. And while there is good and bad shawarma, it is basically the hot dog of the Middle East, gobs of fat and meat strung together. Whether halal or haraam, it's probably not going to be prime rib.
Meat quality has to do with marbling....at least here in the USA.
Highly marbled beef tends to be more tender and tasty than non marbled beef. The taste of meat is in the fat it contains. Fat is marbling. Beef Quality Audits have shown 1 out of 4 Select grade steaks will probably be tough, only 1 out of 6 Choice steaks will be tough. When you get on up to the Prime quality grade, it's practically unheard of to find a tough steak.
IMO, Halal slaughter is inhumane. Under USDA guidelines, a cow is knocked out before her throat is slit and she bleeds out. But the USDA makes exceptions for religions, including Halal. Under those rules, the animal MUST be awake and aware. I'm sure those rules were once because they wanted to be sure the animal was alive and healthy, but today, IMO, there's no such reason to put an animal though that.
To be sure you're getting "better quality" beef, look for Prime beef. There's not a lot of it around in the US. Most of it goes to overseas markets. But some high end, white tablecloth restaurants will carry it. Certified Angus Beef (CAB) is based on the high end of the Choice quality grade. It's much more available and priced more reasonable than Prime.
I doubt the Schwarma you'll find in most restaurants is an especially high quality cut of meat.
I'd give you a general "no." Halal has nothing to do with meat quality or safety, and everything to do with religious belief. Halal meat slaughter is purportedly more merciful than non-halal meat (i.e, there are rules that the animal ought not to see the knife that slays it being sharpened), so perhaps there are fewer stress hormones released if there is a cow of extraordinary IQ being dispatched. It's purported that the blood draining methods result in a more tender product, too, but I've found that tenderness has more to do with freshness an cookng method than slaughter method. JMHO.