Does nitrogen tetrafluoride act as an acid or a base in its reaction with water?
Neither. The reaction is NOT one of ion exchange; it is a redox reaction. Thus, $\ce{NF4+}$ works as electron acceptor here, like this:

$$\ce{NF4+ + 2e- -&gt; NF3 + F-}$$

Since the reaction mechanism is unclear, it is possible that some of its stages may have acid-base character (for example, $\ce{F-}$ sometimes acts as a base), but $\ce{NF4+}$ certainly isn't acting primarily as base or acid here.