In the first rak'ah: after the Takbiratul-Ihram, the recitation of surah al-Hamd and the other surah, there are five takbirs with a final takbir added before going into ruku'.
In the second rak'ah: after the recitation of surah al-Hamd and the other surah, there are four takbirs with a final takbir added before going into ruku'.
Therefore in total there are twelve takbirs: seven in the first rak'ah and five in the second rak'ah.
It is rather the opposite, as we can see that many Sunnis and Shia start the holy month of Ramadhan, and have Eids together on the same day. The issue is that in the Sunni world there is a difference of opinion as to whether the beginning of the lunar month can be pre-announced, or must it be eye-witness.
In Sunni communities there are those who follow Saudi Arabia's announcement, for example, and there are those who follow the local moon-sighting, by the naked eye.
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