Jeff, I'm certain I posted a reply to your question yesterday, but it either got snagged in a SPAM filter or got lost in cyberspace. (Or maybe I was interrupted and didn't hit the reply button...)
At any rate, it definitely depends on the cut of meat. It's been my privilege to barbecue a Wagyu-style beef brisket, and of course, low and slow was the prescription, as it would be for a pork shoulder from a heritage breed pig. A steak under 1-1/2 inches will get the direct treatment, while a thicker steak or tenderloin will be seared over direct heat and then moved to a cooler part of the grill to finish cooking. I am always very vigilant when grilling/barbecuing these
luxurious cuts, and I always keep my trusty instant-read thermometer handy. Heaven forbid I overcook a prime rib roast that cost more than my first car...