Zero-phase windowing - Zero padding at the end of a signal or at middle?

I'm doing an online course on DSP in coursera, where in a lecture the professor says that when zero-padding a signal for FFT it's preferable to do so at the middle of the signal instead of the end. It's also described here; but I can't seem to grasp the utility of this versus zero-padding at the end. I tried plotting the DFT of signals with and without this, but I can't seem to make out any significant improvement in the phase spectrum with or without this. Could anyone here enlighten me?