Here's what a hard proof can do:
If a hard proof and the target is illuminated at 45 degrees it will visually match viewed head on, regardless of the media, if the following conditions are met.
1. That proofed image is within the gamut of the hard proof paper.
2. If unprinted portions of the papers are masked.
3. if the proof and actual are viewed at a distance sufficient that the media texture differences are not discernible.
4. If the proof and actual have some OBAs or substrate that fluoresces then a match requires D50 including D50 uV and the profiles for both generated with M1.
5. If there are no significant OBAs then D50 with or without uV is fine and profiles can be M0, M1, or M2.
6. A match also requires no significant specular reflections which can bring out bronzing or anything that can identify either paper surface as different from each other. Higher illumination of the proof and reference and low ambient lux level and dark clothing can accomplish this.
7. The surround and illumination levels are the same for the reference print and the proof print.
When these conditions are met, the colorimetric accuracy of the profiles is the only remaining variable and, with high quality printers and quality profiles made using the same spectrophotometer instrument it will be extremely difficult, if not impossible, to tell the proof from the reference. Even if one is a matte print and the other glossy. However, creating a hard proof on media with the same charcteristics (glossy, matte, SG, SM, etc) will improve matching when physically handling the media or where one doesn't have the control described.
However, these conditions are not often met and a proof print is NOT the same as just printing each media using Perceptual or Relative Intent even when the other conditions are met.
1. I estimate that Tony met that point 1 condition and Narikin did not.
3. The media textures of the papers mentioned by the OP and Tony are very similar
4. 5. The Epson Proofing Standard paper as used by Tony has a bit of OBA and shows it in the white point. Can do without UV aware profiling I estimate.
6. Epson Proofing White Semi-Matte is not free of bronzing with some printers (Z3200 without gloss enhancer used) but may cope better with Epson printers.
Perpendicular viewing and not too large prints will be enough with the papers described. Yes, 2000 Lux would be best for critical color viewing, going down to 500 acceptable.
7. Identical inks were used on both papers as described by OP and Tony. Observer "metamerism" caused by the inks is unlikely then.
8. addition to point 1; When both the print run paper and the paper to test/proof on have the exactly same gamut in all aspects then all kinds of CM rendering choices and images, in and out of gamut, can be used as long as they are the same for both papers.
9. addition to point 1; When the gamut of the print run paper is smaller and falls totally within the gamut of the test/proof paper then a device-link profile representing the print run paper's gamut within the test/proof paper's wider gamut can be used for the test/proof paper. For the print run paper its equivalent normal paper profile of course. CM renderings should be corresponding. Photoshop CM steps can to a degree simulate device link profiles.
10. addition to point 1; When the gamut of the print run paper is wider than etc. Forget about getting an equal print or one has to compromise on the optimal print possible on the print run paper.
10. Color appearance ........ I might use that argument when the next thread on softproofing is born again, I am usually in the camp that says it is unreliable in reproduction of originals but great when the scene photographed is 5000 miles away.
Met vriendelijke groet, Ernst
http://www.pigment-print.com/spectralplots/spectrumviz_1.htmMarch 2017 update, 750+ inkjet media white spectral plots