Complying to the Sunnah, performing of the Eid Salaah on the outskirts of the town is better and more virtuous, than performing it in the town. 
The Eid Salaah performed in the Masjid is complete, but performing it in the Eidgah is Sunnah. Without any valid excuse, not to read the Eid Sunnah in the Eidgah is contrary to the Sunnah. 
The Eid Salaah should be a huge gathering on the outskirts of the town. In this way the might and power of Islam is manifested. In the big cities it is difficult to make Eidgah on the outskirts of the city, therefore a huge open plain should be chosen for the Eidgah or according to the need, it can be performed in the Masjid, which will be correct. But as far as possible, one huge gathering is more superior compared to many small Eidgahs. 
Performing of the Eid Salaah in the Eidgah is Sunnat-e-Muak'kadah. Without any valid excuse, the one who does not perform his Eid Salaah in the Eidgah is worthy of being reprimanded and taken to task and this kind of a person is a sinner. If the Eidgah is a distance away and it is inconvenient for the old and sickly, then the Jurists have given permission for them to perform Eid Salaah in the Masjid.