In my understanding, Christians never had any call to prayer similar to Azan. In the early Church, different methods were used to call the worshippers: playing trumpets, hitting wooden planks, shouting, or using a courier. Greek monasteries would ring a semantron (flat metal plate) to announce services. By the end of the 7th century, larger bells originating from Campania and Nola were cast. The bells consequently took the eponymous names of campana and nola from cities. By the early Middle Ages, church bells became common throughout the rest of Europe, and were most likely spread by the Irish missionaries and their Celtic influence.
Call to Prayer in jews, known as BAREKHU, has very minor similarity with our Azan. It is opening word of the call to worship at the formal beginning of the daily morning and evening services. The full invocation is Barekhu et Adonai ha-mevorakh (“Bless ye the Lord who is [to be] blessed“). The congregation responds Barukh Adonai ha-mevorakh le-olam va-ed (“Blessed be the Lord who is [to be] blessed for ever and ever“). “Bless,” in this context, is the equivalent of “praise.” Barekhu is also recited by the person who is called up to the Torah reading and is followed by the same congregational response. In some traditions, it is also recited at the end of Service. At one time, It was also used as a summons to recite Grace after Meals. It is more closer to ‘Alhamdulillah‘ and/or ‘Bismillah‘ being recited among Muslims than to Azan.