STFT - Window Functions
This is a rather general answer : I would say that, although each window function has specific characteristics that make it more or less suitable for specific situations, in this context you're not going to see a huge difference in the STFT of a windowed speech signal.

In particular, the two windows that you're comparing are quite similar, so I'd expect that you'd get pretty similar STFT results. You might try two windows that are quite different, like a rectangular and a Hamming or something like that, to see just how much difference those make in your STFT, and then use that difference as a sort of upper bound on the difference that you're likely to see from other windows.