Neural Stack Machines have a slightly more limited memory. Whereas in theory Neural Turing Machines can learn anything, Neural Stack Machines focus on algorithms that are conducive to stacks. Phil Blunsom addresses this some in his recent Russia talk. https://www.youtube.com/watch?v=-WPP9f1P-Xc

actually it might have been his DLSS talk... not 100% sure the talks are very similar... http://videolectures.net/deeplearning2015_montreal/