I found this TruckTrend article on the aerodynamic comparisons between open bed (tailgate up or down), tonneau cover, and full cap.
Their tests held it didn’t matter whether tailgate was up or down.
On the main question, their testing concluded a tonneau and cap offer a similar quantifiable improvement compared to an open bed. There was better drag coefficient (Cd), lower fuel consumption (MPG), and higher top attainable speed.
The idea behind the SnugTop Speed Showdown was to see how fast a truck would go with an open bed, tonneau cover, and a cap. We used a Dodge Ram SRT10.
www.trucktrend.com
This isn’t the last word, but should be considered in the discussion.