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I'd claim any advantage of a circle could be countered by a set of disjoint covering boxes, and the computational cost would be similar.

Quadtree decomposition is only one way to do it.

And decomposing in smaller circles wouldn't lead to a disjoint set.

(Though the "best" approach is probably partitioning a polygon into triangles anyway )

The inherent catch is that we prefer a cartesian system, hence we'll always prefer a compatible coverage if the costs are similar.

Remember that the OP wanted to preselect (spatial index) plausible candidates, how would you do this with circles?

Cheers Rolf
_{(addicted to the Perl Programming Language :)

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