In theory proofing papers have an ISO standard quality control in production and meet ISO media descriptions. Paper white is aimed at the media whites used in different printing technologies so simulations of the other printing technologies are closer in appearance. RIPs used in proof printing (EFI and more) build on that standard with improved calibration methods, dedicated media presets and special profiling. Approved by for example Fogra. Most proofing papers are RC based, they usually have less OBA content than the normal RC papers. Some third party distributors are delivering a normal RC paper, even with high OBA content, as a proofing paper. If I recall it correctly there is some discussion among authorities in the field that the OBA content of proofing papers should be more correlated with the OBA content of the media used in for example offset, gravure, flexo printing.
Dual side coated inkjet proofing papers are not that common. The proof is usually made for color control only. If imposition and register is tested the proof is done on normal dual sided papers or more often the stock used on the press itself. The same for dummies. For example I know the nearby newspaper printer uses leftover roll media from the newspaper press rather than the special inkjet proofing newspaper that exists too.
There are spectral plots of offset papers, inkjet proofing papers and inkjet dual sided papers in SpectrumViz so their media whites can be compared on both Lab numbers and the spectral plots. Texture is a different question but most offset papers are in the smooth category.
Met vriendelijke groet, Ernst
http://www.pigment-print.com/spectralplots/spectrumviz_1.htmDecember 2014 update, 700+ inkjet media white spectral plots