Are there ways stormwater attenuation can be quantified for comparison between different systems or conditions? Various sources agree land cover changes impact the attenuation of stormwater. E.g. forest areas generally slow the rainfall-runoff response and moderate it, reducing peaks in hydrographs, as compared to urban areas. 

Is there a way stormwater attenuation can be quantified, by field measurements (eg. observed streamflow) or model outputs? If so, what are some examples of how this can be done? The reason to quantify attenuation would be to compare differences in attenuation between different basins or between different conditions within a basin.
A typical ratio calculated to quantify this type of response, especially at larger scales (such as for land use changes) is the runoff ratio:

$$R = Q/ P$$

where $R$ is the runoff ratio [mm/mm or dimensionless], $Q$ is the annual flow volume [mm], and $P$ is the annual precipitation [mm]. The runoff ratio is usually calculated for a given data period (multiple years of data) or on an annual basis. It is tricky to calculate for individual events since the antecedent conditions play a large role, but on an annual basis this would be a decent metric to compare different basins or the same basin in time. This is assuming you have a number of years of data to calculate the ratio from.