Sibling rivalry stems out of insecurity and stiff competition between siblings. The best way to curb sibling rivalry is to continuously build up each child and celebrate his or her strengths and differences.
Children compete for your time and attention. When one child feels they have been treated unfairly, it is a better idea to hear them out, rather than just dismissing them as defiant and ungrateful. Having a conversation with them about how they got hurt helps them feel validated that their feelings do matter and will give you the opportunity to hopefully help them see how the scales were not so weighted in one direction.
At times, giving them the opportunity to describe how they interpreted what happened will give you insight as to how they process these interactions and help you determine future courses of action. This may be an easy fix and can prevent future misunderstandings.