Cost History report and Cost Driver History report cannot be directly compared since both reports are from different data-sources
Cost Driver History report is the factors driving the final cost of a private cloud VM or host base on the configuration.
Cost History report uses cost driver's defined cost to calculate the final cost.
In case of CloudHealth vROps integration, we do not calculate the Cost History using cost drivers, instead we collect the data vROps produces and present it in CloudHealth platform