I can't give you a definitive answer on this, but I would check the papers to make sure that they neutralised their extracts before use. Low pH is antibacterial. I know this is trivial, but researchers have been known to overlook such trivialities, particularly when their results appear 'promising'.
I would guess that extraction at acidic pH allows for better solubility for a class of molecules that may have limited solubility at neutral pH, an examples is collagen.
pH affects to the (de)protonation of molecules and it might be affecting to either the solubility and/or the permeability through membranes or channels. Assuming the acidic extract is an extract which you have acidify after extraction.
You might be extracting different compounds in different concentrations too. Given you call it acidic extract because you use an acidic solution for the extraction. If the final pH of the medium is the same the previous paragraph should not apply (if you use the proper control, e.g. dummy acidic extraction)