Praise be to Allah.
Allah, may He be exalted, has promised everyone who believes in Him and does righteous deeds an immense reward in this world and the hereafter. Allah, may He be exalted, says (interpretation of the meaning):
“Whoever does righteousness, whether male or female, while he is a believer - We will surely cause him to live a good life, and We will surely give them their reward [in the Hereafter] according to the best of what they used to do”
The Messenger (blessings and peace of Allah be upon him) also promised everyone who obeys him that he will enter Paradise, as he (blessings and peace of Allah be upon him) said: “Whoever obeys me will enter Paradise.” Narrated by al-Bukhaari (7280).
These texts are general in meaning and refer to rewards for all acts of obedience and worship.
But there are some acts of obedience and worship that Allah, may He be exalted, has singled out and has stated that they have a special reward, such as multiplication of hasanaat (rewards for good deeds), or expiation of sins, or protection from the Fire, and so on.
We do not know of any report speaking of the virtue of the Eid prayer that mentions a specific reward; rather it is included in the general texts mentioned above and others.
The prayer of Eid al-Fitr is included in the general meaning of the glad tidings of success, in the verse in which Allah, may He be exalted, says (interpretation of the meaning):
“He has certainly succeeded who purifies himself
And mentions the name of his Lord and prays”
Shaykh ‘Abd ar-Rahmaan as-Sa‘di (may Allah have mercy on him) said:
“He has certainly succeeded who purifies himself [tazakka]” that is: he has indeed attained victory and gain who purifies and cleanses himself of shirk, wrongdoing and bad characteristics…
With regard to those who interpret the word tazakka [translated above as purifies himself] as referring to giving zakat al-fitr, and interpret the words “And mentions the name of his Lord and prays” as referring to the Eid prayer, although these meanings are included in the linguistic terms, that is not the only meaning.
End quote from Tafseer as-Sa‘di (p. 921).
The prayer of Eid al-Adha takes place on one of the first ten days of Dhu’l-Hijjah, which are days of great virtue; in fact they are the best days of the year.
It was narrated from Ibn ‘Abbaas, from the Prophet (blessings and peace of Allah be upon him) that he said: “There are no days in which righteous deeds are more beloved to Allah than these ten days." The people asked, "Not even jihad for the sake of Allah?" He said, "Not even jihaad for the sake of Allah, except in the case of a man who went out to fight giving himself and his wealth up for the cause, and came back with nothing.” Narrated by al-Bukhaari (969).
It was narrated from ‘Abdullah ibn Qurt, that the Prophet (blessings and peace of Allah be upon him) said: “The greatest days before Allah, may He be blessed and exalted, are yawm an-nahr (the Day of Sacrifice), then yawm al-qarr,” which is the day after. Narrated by Abu Dawood (1765); classed as saheeh by al-Albaani in Saheeh Sunan Abi Dawood (6/14).
And Allah knows best.