Claims for the sonic superiority of SHM-CDs (and the similar Blu-spec CDs and HQ-CDs)—based on the highly touted manufacturing "innovations" employed—are specious at best. I've expressed my skepticism on the matter elsewhere in this forum.
The problem with evaluating them via direct comparison with standard CDs is that the SHM and Blu-spec discs have always received fresh remasterings, so you end up comparing one remastering with another, rather than comparing the two disc-manufacturing technologies.
I have a few of the Japanese-remastered Sony Blu-spec discs of some old Szell Cleveland recordings, and they sound much better than the earlier domestic Sony releases, but they were all DSD remastered in 2008-09, many of them by Andreas K. Meyer, who did the marvelous Bernstein Mahler "Carnegie Hall" box. Interestingly, the 2008 DG SHM-CD remaster of the Karajan Bruckner Symphony box actually sounds worse than the original set. Apparently DG messed up the sound on some of those recordings so badly that no amount of remastering can save them.
The a posteriori portion of my skepticism derives from this test: The claim for sonic superiority of SHM-CDs is based on the use of a new polycarbonate material said to be "more transparent" than traditional CD material, thus allowing your player to read the bitstream more accurately(!) My test was to copy an SHM-CD onto a standard Taiyo Yuden CD-R blank (which does not use the new material) and compare the sound of the two discs on several players and systems. I—and others—found them indistinguishable.
One wag wrote that SHM is an acronym for "Super-High Markup." Caveat emptor.
James
ADDENDUM: In addition to the improved polycarbonate material, the Blu-Spec CD master disc is cut with a blue laser, making the pits and lands of the bitstream "more precise," and the HQ-CD uses a silver alloy in place of the traditional aluminum layer. All three of these new disc types are still considered Red Book CDs in that they are playable on standard CD players.