Are Sunnah prayers obligatory or are they nafl?
No, Sunnah prayers are highly recommended. And Nafl prayers are recommended and added benefit.
On the day of judgement, 1st action counted will be 5 daily prayers, if they are lacking in count or perfection, the Allah will ask to see if My servant has supplementary prayers to make up the weight in positive for a person. Also I have experienced that when I pray supplementary prayers, I feel closer to Allah and I improve my perfection in prayers.
I'm sure there are other rewards, but this is what I can think of right now.
Sunnah prayers are not obligatory. But they are highly recommended because the prophet (saw) used to perform them. They are Nafl or voluntary prayers which were prayed by the prophet (saw), and thus they become his Sunnah for us. If one prays them, he will earn a huge reward from Allah; and if one does not pray them, there is no sin on him.