I have killed quite a few of both and my experience is about the same as the others. I only shoot trophies so I am talking about the large older age class males of each. Moose do not have the tenacity for life as do elk. A moose will pretty much lay down and die if not disturbed where an elk many times will not stop until he physically can not move. I would feel fine shooting a moose with a much smaller rifle than an elk. With an elk you need a big rifle to put him down for good. Sure a high shoulder shot with either and they go right down so I am talking about other hits and shot angles most hunters encounter.
I like the question if elk had the temperament and artillery of a grizzly. I think I would hunt where there were no elk. I don't think you could stop a big bull at close range before you were dead unless you physically broke him down. A shot to the brain or spine.
Most guys elk hunt in Colorado where there are over the counter tags and kill young 2-3 year old bulls just after they become legal. Way different than shooting large old bulls in other states. A large seven plus year old bull is a tough sob with a marginal shot in him.