We published and use the General Purpose and Imagery Reference Overlay. We have really like the color schemes of those basemaps.
The biggest issues with the General Purpose was the readability of the labels, the lack of repeating road names, and difficultly seeing where the city limits end. The labels are a little difficult to read in vector format and they become even more difficult to read once the basemap is rasterized. The lack of repeating road labels made you pan around the map at certain scales to find the name of a road that you were looking at. The transition from "in the city" to "out of the city" is hard to see on some monitors. It would be nice to add a dashed line to clarify the point of transition.
The main things that we changed for the Imagery Reference Overlay were making the road labels repeat, increasing the transparency of the road lines, and enabled symbol levels on the road lines.
We also looked at using Mobile Day, Mobile Night, Public Safety, and Zoning. However, we ended up not using any of them. The Mobile Day and Mobile Night were too difficult to read once rasterized. Our map service for Public Safety would not work properly in our police and fire departments systems and they ended up continuing to use the Esri Streets basemap. The Zoning basemap's road labels were too difficult to read and our users preferred having zoning as an operational layer instead of a basemap.
Going forward, I am trying to convince city administration to allow us to participate in the Community Maps Program so we can just leverage Esri's basemaps but still see our data. I like the symbology of Esri's vector basemaps. The only thing that is missing are address labels, but we can always overlay those ourselves for our maps. I should add that we will not be moving to vector basemaps until they support exporting/printing across most of platform.