I have a couple of pairs of both and, to me, they’re actually really different.
I like the Allbird wool runners for regular day-use. They’re super comfortable and more durable than they look, but the toe box just caved in (my friend Tom says the same happened with his) so after a while it looks like the structure of the wool just broke down and the front lays on your toes. I can see the outline of my foot in the front.
I also have a pair of tree loungers and they are hands down the best house-shoe and bed slipper I’ve ever had. They are also super comfortable and easy to slip on and off. They are also great for travel since they fold up to almost nothing in your roll aboard and they’re great to wear on overnight flights.
My model 000 Atoms are more like actual shoes in that they have more structure, but the material is very breathable and incredibly light. It also has a structured heel in it and I haven’t noticed any collapse in the front like the Allbirds. The stretchy laces make it easy to pull them on and off, and they honestly look great on. I have a pair of the black with white sole and a pair of the all black.
All in, I have over 20 pairs of shoes for work, casual, and special use. Of all of them I probably wear the Atoms about 80% of the time during the day and the Allbird Tree Loungers at night all the time. I suppose if I had to go to just one pair of shoes it would be the Atoms. The Allbird wool runners looked good for the first few months and they’re very comfortable, but after they caved in I stopped wearing them except around the house.
So after all that, despite any price difference, advantage Atoms.