The evidence of those who say it is waajib:

Some of the scholars say that ‘Eid prayers are waajib (obligatory) – this is the view of the Hanafee scholars and of Shaykh al-Islaam Ibn Taymeeyah (may Allâh have mercy on him). They say that the Prophet sallallaahu ‘alayhi wa sallam always prayed the ‘Eid prayer and never omitted to do it, not even once. They take as evidence the aayah (interpretation of the meaning), “Therefore turn in prayer to your Lord and sacrifice (to Him only)” [al-Kawthar 108:2], i.e., the ‘Eid prayer and the sacrifice after it, which is an instruction, and the fact that the Prophet sallallaahu ‘alayhi wa sallam ordered that the women should be brought out to attend the ‘Eid prayers, and that a woman who did not have a jilbaab should borrow one from her sister. [See Tamaamul Minnah: by Al-Albaanee: p.344. Refer to Al-Mughnaee by Imaam ibn Qudaamah: vol. 2, p. 223.]

The evidence of those who say it is Fardul Kifaayah: Some scholars say that Eid prayer is Fardul Kifaayah. This is the view of the Hanbalees. Refer to Al-Mughnaee by Imaam ibn Qudaamah: vol. 2, p. 223.

The evidence of these who it is sunnatul Muakkadah: A third group say that ‘Eid prayer is sunnah mu’akkadah. This is the view of the Maalikis and Shaafa’is. They take as evidence the hadeeth of the Bedouin which says that Allâh has not imposed any prayers on His slaves other than the five daily prayers. Refer to Al-Mughnaee by Imaam ibn Qudaamah: vol. 2, p. 223.