Essential Formulas, www.essentialformulas.com
, who makes my favorite probiotic (the 12+ probiotic professional formula in the GREEN box, not the original formula in the navy blue-ish box), goes out of their way to specifically state that there are NO HSOs in their product.
I do believe one of the reasons that dogs (and animals in general) don't tend towards GI problems like humans do is because they are constantly exposed to HSOs and bacteria in general through licking and sniffing the ground and everything on it. We don't do that, thus more gut issues, especially post-antibiotic use.
I also would guess that the probiotics grown on cultured vegetables would either be HSOs or very close relatives (based on the fact that veggies grow from the ground). So I guess I do get both types (HSO and non-HSO through the cultured foods in my diet (cultured veggies, kombucha, raw acv, probiotics, and some kefir as a treat on rare occasions).
I will admit that I don't know the difference between HSOs and non-HSOs, as when I've looked at the list of bacterial strains, many seem to live on both sides of that fence. I could be completely wrong about that.
With the lack of independent research, I don't know what to say in terms of the superiority of one or the other.