Which is more befitting for a fasting person sitting in the mosque during the adhan: to pray Tahiyyat al-Masjid (greeting of the mosque) so he can drink while sitting, or to drink while standing so he can achieve the virtue of hastening the breaking of the fast?

It is recommended to hasten breaking the fast after confirming sunset. It is permissible to drink while standing, although it is not the preferred manner, as there are Hadith narrations that prohibit it. If a fasting person enters the mosque at the time of the Maghrib Adhan, it is best for him to promptly break his fast while standing, then pray the two Rak'ahs of تحية المسجد (greeting the mosque). If he sits to drink his iftar, then stands to pray the greeting, there is no harm, as it is a light sitting that does not invalidate the purpose of the greeting.