MOST scholars, from the fatawa quoted below, say that the order of preference for sacrifice is: camel, cow, sheep, and then a share in a camel or cow.
They base it on the hadeeth of the Prophet ﷺ concerning Jumu’ah: “Whoever comes at the earliest hour, it is as if he sacrificed a camel. Whoever comes in the second hour, it is as if he sacrificed a cow. Whoever comes in the third hour, it is as if he sacrificed a horned ram. Whoever comes in the fourth hour, it is as if he sacrificed a chicken. Whoever comes in the fifth hour, it is as if he sacrificed an egg.” [Al-Bukhari, #881; Muslim, #850]
Imam Ibn Qudamah (d. 620AH/1223CE) says in Al-Mughni, the most widely known textbook of Hanbali fiqh:
“The best sacrifice is a camel, then a cow, then a sheep, then to have a share in a cow. This is the view of Abu Haneefah and al-Shaafa’i
[…]
“A sheep is better than sharing in a camel, because the aim of the sacrifice is to shed blood. A ram is better than a sheep (ewe), because that is what the Prophet ﷺ sacrificed and the meat is better.” [al-Mughni, 13/366]
Al-Lajnah Ad-Da’imah [The Permanent Committee for Islamic Research & Fatawa of Saudi Arabia] said after expressing a similar opinion:
“This is the view of the three imams – Abu Haneefah, al-Shaafa’i and Ahmad. Maalik said: The best is a young sheep, then a cow, then a camel, because the Prophet ﷺ sacrificed two rams, and he ﷺ did not do anything but that which was best.
“The response to that is that the Prophet ﷺ sometimes chose the option that was not the best option out of kindness to his ummah, because they follow his example. He ﷺ did not want to make things difficult for them. He stated that the best is a camel, then a cow, then a sheep, as stated above [i.e. the hadeeth]. And Allah knows best.” [Fataawa al-Lajnah al-Daa’imah, 11/398]
Ref: IslamQA
Dr. Bilal Philips