Which is better and closer to the the Sunnah: to perform the two rak'ahs before Fajr (Sunnat al-Fajr) in the mosque or at home? And what is the evidence for that?

The Sunnah is to pray the two rak'ahs of the Fajr supererogatory prayer at home, based on the Prophet's (peace and blessings of Allah be upon him) saying: "The best of a man's prayers is in his house, except for the obligatory prayers." This is what the Prophet (peace and blessings of Allah be upon him) himself did. It is permissible to pray them in the mosque, but praying them at home is better.