I'm also perplexed (schematics notwithstanding) about the differences between the two products/links from electricheap and dfrobots, they look very similar to me. I think I found the link to the manufacturer, not very informative I'm afraid but with larger pictures.
http://item.taobao.com/item.htm?spm=a1z10.3.w7504506493.3.0QqHPb&id=13338760752A question: shouldn't pitch detection be performed in the ADC? Assuming that the output of the external device is just an amplified signal (unfiltered), roughly corresponding to the output of the mic, in order to get the pitch one needs to sample the signal.
Then, shame on me, I don't know how many samples would be necessary to detect, say, a 440Hz frequency with good approximation, it's a very simple calculation but I don't remember the parameters to be factored in. But if, let's say, we needed just 880 samples / second, it would probably be within the reach of a program running on an Arduino.