They have pros and cons. If any system worked for all tanks, everyone would just set up that system and have no troubles.
Some of our tanks here are ex ATS.
One of the cons of an algae scrubber is the messy algae from the screen getting cast around the tank...ie the ATS made things worse.
One of the problems with a refugium (variation on ATS, same plant binding action) is it didn't work to control non nutrient based invaders like red turf algae/bryopsis
Additionally, you've never seen a long term pico reef with an ATS in the classic sense because smaller tanks will become wrecked with the green slime and mat algae that proliferates on the screen due to small physical volume.
The peroxide system is closer to using clean up crews...an after the fact approach mentioned in the first pages. This is an option for simply killing algae, never having it in the tank option.
In my systems that are incredibly small I don't want plumbing and HOB clutter an ATS would require, so that's why I'll never use one.
Having seen most aspects of pico reef design, I've never seen a better method for algae control than a drain and treat. One day there will be a better method that makes a gallon reef last longer than 7 years...when that technique comes, peroxide will be a technique of the past!
Yellow, doc-laden water is another tenet of the Adey ATS system in some tanks, charcoal counter filtration has its own issues for some keepers (hlle is one)
ATS have many success stories, they are valid options to try at any time.
All the large tank work we do is a branching off that, the initial focus was pico reef longevity.
I do believe ATS systems have success in larger tanks, any one here with red brush algae or bryopsis is welcome to set one up and post before and after pics while we compare cure and sustain timelines!