I don't think Hotel will always beat the booking price, but does no harm to check, as they are on booking sites to get publicity and obviously, they have to pay the booking sites commission on bookings.
We stayed in an Hotel in Istanbul, we paid cash got 10% off the price and we did check it on on booking sites, but it as cheaper to book directly. Before we left, they told us always to contact them for a price if we were coming back.
We have just dealt directly for a place next New Year, again cheaper by contacting the accommodation directly.
I can only speak as we have found.