Out of the British Overseas Territories, only Gibraltar is in the European Union. Akrotiri and Dhekelia is also in Europe, at least according to the EU interpretation of admitting Cyprus as a member state. Then why is the British Overseas Territory of Akrotiri and Dhekelia treated differently from Gibraltar?
As pointed out in the Wikipedia article that you point to Governance they are military bases only. Gibraltar on the other hand is a member under special rules covering its status as a colony of the UK. Gibraltar is not a member in the sense that the UK or France are members.
Gibraltar is a British overseas territory. The British Nationality Act 1981 granted Gibraltarians full British citizenship.
The governor enacts day-to-day matters on the advice of the Gibraltar Parliament, but is responsible to the British government in respect of defence, foreign policy, internal security and general good governance. Judicial and other appointments are made on behalf of the Queen in consultation with the head of the elected government.
Gibraltar is part of the European Union, having joined through the European Communities Act 1972 (UK), which gave effect to the Treaty of Accession 1972, as a dependent territory of the United Kingdom under what was then article 227(4) of the Treaty Establishing the European Community covering special member state territories, with exemption from some areas such as the Customs union and Common Agricultural Policy. After a 10-year campaign for the right to vote in European elections, since 2004 the people of Gibraltar have participated in elections for the European Parliament as part of the South West England constituency.
The United Nations Committee on Decolonization includes Gibraltar on the United Nations list of Non-Self-Governing Territories. Gibraltar has been on the list since December 1946.
The basic philosophy of their administration was declared by Her Majesty's Government in 'Appendix O' to the 1960 treaty with Cyprus, which provided that the British government intended:
Not to develop the Sovereign Base Areas for other than military purposes.
Not to set up and administer "colonies".
Not to create customs posts or other frontier barriers between the Sovereign Base Areas and the Republic.
Not to set up or permit the establishment of civilian commercial or industrial enterprises except insofar as these are connected with military requirements, and not otherwise to impair the economic commercial or industrial unity and life of the Island.
Not to establish commercial or civilian seaports or airports.
Not to allow new settlement of people in the Sovereign Base Areas other than for temporary purposes.
Not to expropriate private property within the Sovereign Base Areas except for military purposes on payment of fair compensation.
The ancient monuments and antiquity (in particular the site and remains of Curium, Sanctuary of Apollo Hylates near Curium, the Stadium of Curium and the Church and remains of the Monastery of St. Nicholas of the Cats) will be administered and maintained by the Republic of Cyprus. Licences for antiquity excavation will be issued by the Republic but will be subject to the consent of the authorities of the Sovereign Base Areas. Movable antiquities found in excavations or discovered will be the property of the Republic.