AT vs MT goes back to when Moses shipped his first surplus Willys back home in a crate.
The difference is marginal for most of us. For their specific task, mud, soft snow, deep sand, loose roots and dirt the MT tread will excel. On slickrock probably too, where pattern and sipes don't matter much.
There's times MT will be worse, like pavement, gravel, hard snow, etc. That's why an All Terrain exists. It's equally marginal all the time. It's not that most ATs can't do mud and snow, it's just that they aren't great in it. It's still usually a pretty aggressive tread.
So it boils down to opinion mostly. My $0.02 is it's pretty rare I find a time when I wish I had an MT and when I do a set of tire chains go on. That is better than an MT for those times. The rest of the time the noise, the slipping on the highway. Not worth it. But I also don't go looking for super hard trails all the time where living daily with an MT is just the price you pay to play.
Now the sidewall angle, there is something to that. I'd run a strong AT over an MT with weak sidewalls just about any day. There's a downside to 3-ply in ride quality, MPG and such. So that is a trade-off I am willing to live with. I've sliced sidewalls on otherwise technically mild roads. I can overcome traction challenged ATs with lockers, winch, lower air pressure. Walking 50 miles is a bigger drag to me. That possibility was on the table when I had two flats (in 3-ply BFGs even) on the shale road to Toroweap but a handful of tire plugs held well enough.