Which valve should be operated more frequently, a gate valve or a butterfly valve.
Supplemental to what David has said, A butterfly valve especially in what seems described here as an AWWA application will >usually< be rubber-lined and as such the scale will fracture and dislodge when the valve cycles.  It is advantageous with a butterfly valve to install with the stem horizontal, and for the vane to open so that the bottom edge moves upstream.  This will fracture/dislodge the layer of sediment/scale at the bottom of the pipe and the particles will be flushed away by the initial high-velocity flow as the valve begins to open.  Another advantage of mounting BFVs with Horiz shafts is that the bottom bearing is not sitting in a puddle of sediment and the valve lasts vastly longer. 
I have never had personal experience with a gate valve that does not leak, and crushing scale between the seats and disc will not contribute to improving the surface finish hence leak resistance  of the valve.

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