This excerpt is taken from Sheikh Zubair Ali Zai Rahimahullah's Book on the Rules and Issues of Qurbani.
Question:
Is sacrificing on the first day more rewarding and superior, or is the reward the same for all three days? Please explain.
Reference: (Zafar Iqbal Shakargarh)
Answer:
The Messenger of Allah, peace and blessings be upon him, said on the day of Eid al-Adha: "Today we will first perform the prayer, then offer the sacrifices."
Reference: (Sahih Bukhari, Book of the Two Eids, Chapter: The Sunnah of the Two Eids for the People of Islam, Hadith 951; Sahih Muslim, Al-Adahi, Chapter 1961)
From this hadith, it is established that the Prophet, peace be upon him, sacrificed on the first day. Therefore, it is best and preferable to offer the sacrifice on the first day of Eid al-Adha, i.e., the 10th of Dhul-Hijjah, and it is permissible and rewarding to sacrifice on the remaining two days.
Sayyiduna Abdullah bin Abbas, may Allah be pleased with them both, said: "There are two days after the day of sacrifice for offering sacrifices, and the best sacrifice is on the day of slaughter (the first day)."
Reference: (Ahkam al-Quran by Al-Tahawi 205/2 Hadith 1571, and its chain is Hasan)
Reference: (Shahadat, August 2000)