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Hoerner's Fluid Dynamic Drag book is the bible for aerodynamics of aircraft, and has a section on various drag profiles of landing gear and wheels. Smoother is by far better, as seen in the tests noted above.
A few years ago, about 30 of us with Porsche 944 cars did a 500 mile ratrace through the interior of British Columbia, at speeds, ah, well above posted limits. The cars, being all 944s, had identical sheet metal and shape. Various wheels made a radical difference in slipstreams, as seen by the mist thrown out at high speeds on wet roads.
My car has Porsche Design 90 wheels, basically shaped on the outer surface like the pizza pan thing, but with vent slots forming 7 short, wide spokes out near the rim. Other cars had the whole range of Porsche and aftermarket more radically spoked wheels. My car had little visible wake, but the more radically spoked-wheel cars threw out a lateral column of mist ~3' out into the slipstream along the sides of the car. In other words, those radically spoked wheels, in effect, made frontal area of those cars about twice as wide, i.e, the hole punched in the ambient air was much bigger than the smooth-wheeled car.
As it happens, the disk-shaped wheel is likely to be lighter than a spoked wheel, and to have its mass closer to the center. This means less energy to accelerate and decelerate such a wheel, i.e., better fuel economy and braking on that account, too.
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