According to Hanafi fıqh, you should join Jama'at because of this hadith:
إذا أقيمت الصلاة، فلا صلاة إلا المكتوبة
When the Iqamah is called, no prayer should be performed except the obligatory prayer. (Riyad as-Salihin)
However, it is considered that this hadith involves prayers other than Fajr prayer because of it's virtues which are explained in some other hadiths.
So, for Fajr prayer, if you think you can catch the Jama'at even at the last sitting, you should first offer sunnah. On the other hand, if you are not sure to catch the jama'at, you skip the sunnah and join the Jama'at.
I should also add here that, while you are praying four-rak'a-sunnah (confirmed or nonconfirmed), you can finish your prayer after first sitting (that's after two rak'as) if the jama'at starts praying. if you standed up for third rek'ah and didn't reach to its Sujiud, you can make ending salam when you are standing; but if you reached to Sujiud of third rak'a, you complete your prayer to four rak'as.
Now, what do you do if you cut sunnah prayer two rak'as earlier or if you don't even start to it in order to join jama'at? You can offer the sunnah just after farz. This is for zuhr (or Juma), asr and isha. You can't pray nafilah after fajr prayer and after asr prayer because of makruh times (the ones for nafilahs in this case).
I wrote from "catching the farz" part of the Turkish book named Ni'met-i İslam.
The explanation about Fejr prayer above is for the person who couldn't pray it at home. Praying sunnah of Fejr at home is better than praying it at the Masjid. The Prophet may peace and blessings be upon him prayed sunnah at home and doesn't tolerate who is praying it at the Masjid. If you are to pray it at the Masjid, you should pray on a place far from the rows of the Jama'at. For other sunnah prayers, there are different views whether it is better to pray it at home.
The case of Juma prayer also needs an explanation. In the Juma prayer, there is khutbah before Jama'at. So, you skip sunnah prayer if the khutbah starts in this case.