Putting on my outdoorsman hat, just trying to figure out why birds would roost or linger on one statue and not another. In looking at your example pics Curt I notice the statue with the larger/higher base is the one you mentioned is ignored. I wonder if this is related to the proximity of the statues to any possible food source?
Consider a lower situated statue in parks and so forth which would provide a suitable roost for observing and quickly reaching crumbs, scraps of food dropped by passers-by but yet still provide a level of elevated protection against ground-bound predators. A broader base may also further remove benches where those scraps are likely to be dropped.
I wonder if there is a correlation? Not something for a gov't grant study but sure is a curious thing. We need that wildlife guy from the Geico commercials.