Praise be to Allah.
What matters with regard to breaking the fast is the setting of the sun, as the Prophet (peace and blessings of Allaah be upon him) said: “When the night comes and the day departs, and the sun sets, then it is time for the fasting person to break his fast.” Narrated by al-Bukhaari (1954) and Muslim (1100).
There is nothing wrong with relying on the adhaan of the muezzin for breaking the fast, because it is most likely that he is basing it on the setting of the sun. Some muezzins delay the adhaan a little bit in order to be on the safe side for those who are fasting. This is a mistake and is contrary to the Sunnah as we have stated in the answer to question no. 12470.
If your city follows the broadcast adhaan, then it is better for you to follow the broadcast adhaan too, because it is more precise.
And Allaah knows best.