I have been in both camps. But when it comes to putting the game down, you MUST be ready to follow-up. Let me set a scenario...
8 does feeding in a field about 130-150yds off. My wife's first actual animal. I kept my scope on the doe she chose, she fired, the doe hunched up, took a few steps, and laid down. I shifted my sights to harvest one myself, when she told me that it had gotten back up. I tried to find her, but the deer were now milling about too much and the entire herd left the field. Short story, lost the deer. Since then, if a second shot remains, we take it.
Last season, cow at 260yds+/-. 165gn bulk Remington cup and core, 2600fps. Heart shot. She swapped ends and headed for the trees, slowly so I knew I had hit her good, but I was not going to let her get into the trees, so when she got to the woodline, she stopped and I put one through her shoulders, BOTH SHOUDERS, she laid right down, but her young brother got her up again!! I ran forward, just as she took a step in the woods. She just stood there, head down, not wanting to move, but only offering a texas heartshot. At about 100yds, I dropped to a knee, yelled and she looked back at me and got one between the eyes. Still took me 2 hours to get her gutted and out of the woods, and I STILL had to cut down a tree to get her out!!
Gutting and skinning told the story of the hits, each one was a decent kill shot, but things happened. If I had held to my old rule of one shot, I would have still had a moose, but it would have taken all night.