I have girls, but they want to do those same things - at that age, the older one always had to one-up the younger one. On some level, the older one WILL always one-up the younger, if only because they're older and have more life experience. However, knocking down a smaller child simply because you can is NOT okay, and has to be dealt with so as not to recur. When my older daughter would knock her sister down, I'd stop her, drag her over to little sister, pick up little sister, and big sister would have to apologize and then walk in the door AFTER her sister. In other words, if you think you're going to knock down the little people so you can always be first, not only do you have to go all the way back to where you started, but now you have to let the little people go first. At the very least, she has learned that if she's going to be first, she'd better make sure she has a clear shot at the door!
It's fine to be competitive, but it's not okay to flatten your sibling in the process! Kids just have to learn it by being forced to make amends, over and over, until they get it. At this point (they are 9 and 6) I can usually give my older daughter "the look" and she will catch herself before she does anything too crazy to her sister. They do learn not to injure each other (physically, anyway), but it takes forever! LOL