It runs on SSE2, but can't go beyond that.
I'm using 1888 btw.
Despite the similarity of the names, SSE3 is unrelated to sSSE3 and the same is true for SSE4a and SSE4.1.
AMD has to date not implemented the SSSE3 and SSE4.1 instruction sets on any of their CPUs.
Therefore the recommended GSdx version for AMD users is the SSE2 one.
There is a minor speed loss, but it is only about 10% overall.
Shadow Lady: I knew the SSE moderation tool would come in handy