For bulk operations in index order a larger page size can give a noticeable, sometimes significant, performance increase. For very random access, particularly many small writes, there is similar potential for significant performance reduction.
A single read of a 16K block will take four times longer than the read for a 4K block, assuming the drive heads are in the right place at the time, but reading four sequential 4K blocks will be almost the same as reading a single 16Kb one.
Unfortunately it isn't something we can give you more precise advice on, especially without a lot of information about your application's I/O patterns - it is something that you probably need to benchmark with your specific application in your test environments to be sure about.
4Kb is usually picked for the default (at least on x86 or a64 based CPUs) as it matches pages sizes in the underlying OS and sometimes hardware so in the general case is more efficient because it is the "natural size". DB specific considerations override this though, which is presumably why MS SQL Server uses 8Kb page sizes.