Actually, Minorca was considered a more strategic base than Gibraltar. During the chaos of the American War of Independence, when Spain and France were both supporting the Americans, the British government was willing to return Gibraltar to Spain in return for their neutrality (and a gaurentee that Florida would remain British). Possible PoD, no Treaty of Amiens (negotiations collapse), and Minorca is succesfully defended throughout the alt Napoleonic wars. Or maybe it's just not in the treaty to start off with.
Minorca provides Britain with a major port in the Western Med, and is the next stop after Gibraltar of the sea routes to India (Gib, Min, Malta, Alexandria, Suez, Aden, Bombay). Though we're unlikely to see our WWII with these butterflies, if we keep them to a minimum, then the alt WWII would see (in all likelyhood) Minorca siezed by Vichy France/Italy, and relieved via Spain. Interestingly, we may see the suggestion that the free French fleet in Algiers sail to Minorca.
Later, Minorca would probably go the same way as Malta.