All depends on the situation and type of terrain.
If there is snow on the ground I will take most kill shots, pretty hard to lose an animal in the snow.
Where I live there is very little open country, its all thick bush, alder and mountains. If an animal is going to run after a shot you can guarantee its going to be downhill and into the thickest brush you have ever seen. Tracking in thick brush is very very very hard, especially if there is a lot of game sign in the area to start with.
In situations like this its nice to be able to put the animal down on the spot, eg: head shot.
I have cut a lot of wild meat and personally I am sick of working through blood shot front quarters, I am starting to head shot more game, and have been on quite a few buddies hunts where they head shot the animals as well. Out of all the animals no one has missed or wounded an animal. Absolutly every one has been a bang/flop and no meat wasted what so ever. And only one set of antlers busted apart

time to break out the epoxy.
If you take the lung shot and the animal reacts but justs stands there bleeding and milling around, just let him fall. If you hit him solid then just let him fall down. Another shot could supercharge him.
If he starts taking off and is going to go out of sight then keep shooting. More holes equals more blood and shorter distance to recovery.
A good second shot on the moose would be the hump shot, aim approx 6 inches below the highest spot on the hump. That is where the spine is.
If you bone out the animal you'll see that the hump is like a bone fin coming off the spine. It is possible to pass a bullet through the hump if hit high enough and not break the spine, he might drop but keep on him because he could get back up again.
If you have a backup shooter and you are both aimed on the moose I would go for the head shot ( given the distance isn't too far and you are confident you are going to make the shot).
Either way if you lung shoot a moose, and you are certain of a good shot than the moose will die. No questoin about it. The question is how hard do you want to work after he is down. Moose seem to get a lot bigger when you start to try and move them.
Hope this helps and good luck with your moose
Brambles