Sibling rivalries can be really hard to handle. I've had a hard time with my son and daughter fighting constantly. It may not be what you want to hear, but honestly it just takes time. Once my kids started to mature, the fighting and rivalry died down. Until then, keep tabs on the rivalry to make sure that it doesn't become permanent. When it seems like one of the kids has taken it too far, make it clear that what they did wasn't okay. Have them apologize to their sibling, and put your foot down when it comes to competitive behavior for the next few days. Encourage your kids to focus on competing with themselves instead of each other.
I personally have a twin brother so I know all about sibling rivalries! What I never thought would happen when I was little is my reality now-- my brother and I are best friends! This happened after college and now our kids are friends too.
How old are your children? My eldest daughter and son are two years apart and they often fight because they are so close in age. In comparison, my daughter and youngest son are further apart in age and they have more of a mentor relationship because my youngest looks up to her and she looks after him.
It is world war between my two daughters who are two years apart, too and the fighting can sometimes get physical. The funny thing is after the fight (and after I get really angry at them), they end up all chummy again. My youngest gets along well with both older sisters and never really gets into fights with them. So I guess age difference has a lot to do with sibling rivalry.