It is allowed for a person to cut his hair after he has sacrificed (or after the sacrifice has been done on his behalf) even if that is on the day of ‘Eid.
And a whole ram is better to sacrifice than sharing in a seventh of a cow or a seventh of a camel. However, if a person was to sacrifice a whole camel or a whole cow, then the fuqahā (jurists) have stated that that is better than one sheep (or ram).
Shaikh Ibn ‘Uthaimīn (rahimahullāh)
(As’ilah wa Ajwibah fī Salātil-‘Eidayn, p. 17)