I occasionally send files to a print lab (WHCC) when I need prints larger than I can make at home (Epson R1900). They use a process where they expose the image from a digital file onto chemistry-based photo paper, which is then developed in the traditional manner.
I recently did a shoot at Portland's Rose Test Garden and got some nice images of roses. When I went to soft-proof the images in Lightroom 5, using WHCC's ICC profile, the results were really muted in the reds, oranges and yellows.
I keep my monitor well-calibrated (dE between 1 and 2), and for prints on my Epson R1900 the soft-proofing display looks really close to the resulting prints.
I decided to send WHCC two of the images, ones that soft-proofed much worse than my R1900, expecting that I was seeing the effects of a bad profile (I re-downloaded and reinstalled the profile anyway just to be sure). The files were in the Adobe98 color space, with an embedded profile.
The resulting prints look almost exactly as displayed in the soft-proof: unacceptable desaturation of reds/oranges compared to the original images and inkjet prints. It appears that WHCC's digital-to-photo-paper print process has significantly narrower color gamut on the red/yellow side. This does not appear to be the case for blues and greens.
I'm confident that my color-management setup is correct, as I always get consistent soft-proofing on prints from my Epson inkjet, and the soft-proof display for WHCC's profile matched their prints to the same degree (i.e. almost perfectly).
I've always believed that chemistry-based photo paper would have a wider gamut than inkjet printing, but this conclusively demonstrates that I was wrong.
One possibility is that the R1900, which has red and orange inks in addition to CMYK, is just naturally going to be better at that end of the spectrum.
Here are screenshots (from Lightroom) of the three soft-proof images (original full-gamut from raw file, R1900 soft-proof profile, WHCC soft-proof profile). Since the soft-proofs mirror the printed results well I'll assume they can be a proxy for the prints. I have no idea how these will appear on other monitors in absolute terms, but you should be able to see a slight difference from the original to the R1900, and a large difference between the R1900 and WHCC soft proofs.
So, the question is: Is it true that chemistry-based paper prints have been surpassed by inkjet prints in terms of color gamut?