The main different between aniracetam and piracetam is the metabolization rate. Aniracetam is argued to be much more effective and fat soluble but has a shorter life span in the body. Piracetam is known to be less effective but is water soluble and has a longer - about 4 hours - effective time.
The category of "cognitive function" is generally pretty broad, and memory is generally accepted to fall under it. (I'm a neuroscientist, but if you don't trust me, do a Google search.) Memory without some kind of qualifier is not a particularly term either, since there are at least three forms of memory with distinct neural substrates.
FWIW, the closest thing I can find to a human study is http://www.sciencedirect.com/science/article/pii/00913057859..., which might indicate attention and/or working memory enhancement in non-human primates, but I don't have full text access. There are also a bunch of studies showing it enhances long-term memory in rats, but rats are not primates.
