Australian consumer affairs show The Checkout from ABC, just created an OTA-parity explainer video of biblical proportions.
As part of their research they called a number of hotels to see if they could get a better rate direct. The calls worked and they give consumers a clear and simple recommendation: book direct for the best price.
As an aside, my hit rate when calling hotels in Europe and the US for a better rate is probably 50/50. I am afraid to say that sometimes I have found reservation agents recommend that I go to the OTA to make the booking. A little internal training is probably an easy-win for most revenue managers.