Hermitian FFT vs discrete Fourier transform. Python's $\tt hfft$ vs $\tt fft$
You have to understand that fft is the general function, which always works. hfft, fftr and their derivatives are optimized for special signal constellations and should either be faster or more accurate (if this is at all necessary with modern floating point accuracy).

The hfft function is used, when you expect the spectrum to be real-valued. This happens, if your input signal has even symmetry. I doubt that your audio signal does have this property. Have you been looking for fftr (i.e. fft for a real-valued signal)?

In case your input signal has the even symmetry property, the output of fft and hfft should be exactly the same (up to numerical residual errors). Also, hfft should be a bit faster in this case (otherwise, it would make no sense to use it).