The relative status of the British Crimea versus the Sardinian Crimea medals has been well discussed by Ulsterman & Elmar Lang. A.R. Margrave of the Crimean War Research Society (UK) has written much about the British Crimea medal awarded to the French & Sardinians. He quoted original Foreign Office & other archival correspondence which pointed out that Queen Victoria intended to apply the same medal qualification to the Allies as for British forces. The British medal was to be awarded only to those active British & Allied personnel who had arrived in the Crimea on or before 9 September 1855, which date marked the capture of Sebastopol. Late arrivals after 9-09-1855 did not qualify for the British medal. So it would appear that one purpose of the Sardinian Crimea medal was for award to the Sardinians arriving too late for the British medal.
A second purpose for the Sardinian medal arose from the British decision to ship only 15,000 British Crimea medals to Sardinia, according to Margrave's research. It has been pointed out that the Sardinian Expeditionary Corps amounted to 18,000 men, and by the end of the war had further grown to an estimated 21,000 men. The Sardinian Crimea medal would have compensated for the inadequate supply of British medals for Sardinian veterans who had arrived in the Crimea before 9-09-1855.
There is a handsome certificate from the Sardinian War Ministry that accompanied the British Crimea medal awarded to Sardinian troops. Perhaps some of you have seen or own an example. My photocopy of one such is made out to Grenadier Francesco Morini of the 2nd Regiment of Sardinian Grenadiers, dated 15 June 1856 at Turin.