When we reconcile with our brethren, we receive a temporary peace, our peace of mind. But what Jesus offers us is much more. It is the ultimate peace in our hearts, knowing that our broken relationship with The Father has been fixed by His death on the cross.
Jesus was amongst the crowd preaching when someone told him that his mother and brothers (and possibly sisters) were standing outside and wanted to speak to Him. I have always wondered why did they not come in? Or why did Jesus not go out to meet them but used them to talk about who all constitute as the family of Christ. But when we read the same incident in Mark we get to know the context of the situation.