AUS 8 (aka 8A) has one huge similarity to ATS-34, in that they are both steel. On the other hand, if you're a nit-picky knife knut, the two steels are a bit different. Performance-wise, here is my opinion of the main differences you'll see. ATS-34 will almost always hold its edge longer, because it is usually harder (stronger) than 8A, and because it's more wear-resistant. 8A will be easier to sharpen, for both of the preceding reasons, and because it is extremely fine-grained, and some people -- myself included -- find putting a razor edge on a fine-grained steel generally easier.
I can drop down further if you'd like ... ATS-34 can get harder than 8A because ATS-34 has more carbon, and ATS-34 is more wear-resistant both due to hardness and due to the amount of carbides. 8A is more fine-grained due to the addition of a small amount of vanadium.
8A, and all the AUS series steels (AUS-4,6,8,10) are Japanese.
Generally, 8A is one of my favorite "2nd tier" steels, mainly because it can hold its own with most of the other steels in its class, and is so easy to put a scary sharp edge on. Steels like VG-10, ATS-34, S30V, etc., are definitely a step up from 8A.
Joe