Perhaps this is because there are fewer exterior 'walls' in American suburban gardens. The spherical sundial or 'armillary' is a somewhat more complicated and visually interesting model. So a 'true armillary' is an elaborate globe of revolving, nested spheres and ringed orbits. Ornamental and historically interesting, but not a timepiece. What serves as a sundial today is a modified armillary.
More complex ones have additional bands which represent the solstice and equinox positions.
Armillary-spheres are manufactured of lead, cast bronze, brass, aluminum or iron. They tend to be more expensive but showier and more commanding ornaments than flat or vertical sundials. Combination sundials combine a flat style with a birdbath basin. Vertical dials can also announce a street address or residence nameplate. However they came be more accurate based on how closely the angle of the gnomon off the horizontal plane matches the angle of your latitude position.