Which is more proper: completing the funeral prayer being performed in a public place, or leaving it and going to the mosque to catch the congregational obligatory prayer?

It is disliked to depart from a funeral before praying over it. You should pray over it with the congregation to earn the reward of congregational prayer and the funeral prayer. The general rule is to pray the obligatory prayer first, unless there is a concern that the deceased will decompose, in which case the funeral prayer is prioritized, as long as the time for the obligatory prayer has not expired. If two prayers coincide, the one more likely to be missed is performed first. Regarding the Fajr and Asr prayers, the funeral prayer is performed first to avoid praying over the deceased during the forbidden times. As for the Maghrib prayer, the funeral prayer is delayed unless there is a concern about the deceased decomposing.