I've not used the non tallow AOS, but the old tallow AOS is fantastic (I am rationing my one puck). That said, it is ridiculously overpriced and even if they made it, I wouldn't buy more. I think the following all perform nearly as well, if not as well, for much less coin:
Barrister and Mann
Mike's
Petal Pusher Fancies
DR Harris (though I find its performance a little erratic for some reason)
Haslinger Schafsmilch (probably spelled wrong)
Klar Kabinett would be on there too, but it's discontinued. My understanding is the other Klar Soaps are good performers, but they are fairly expensive.
I'm sure there are others, but these soaps are all great performers for me. You'll note: they have absolutely nothing in common in terms of ingredients or form, but they all perform really well.
Barrister and Mann
Mike's
Petal Pusher Fancies
DR Harris (though I find its performance a little erratic for some reason)
Haslinger Schafsmilch (probably spelled wrong)
Klar Kabinett would be on there too, but it's discontinued. My understanding is the other Klar Soaps are good performers, but they are fairly expensive.
I'm sure there are others, but these soaps are all great performers for me. You'll note: they have absolutely nothing in common in terms of ingredients or form, but they all perform really well.