Court of Arbitration is surely more powerful than FIFA in many things, and they can check documents and things related to this case which is good for all because as right now things are going most chances they are not going to change this decision because Ecuador is already complete their all legal things which give them good advantage in FIFA, and surely they are going to do same in this Court as well which is clearly giving them advantage.
Chilean is soccer crazy nation, and they are trying their best for having any chance even they lost in ground and now just because of one doubt they are creating some hype which is not going to help them for having any chance into this event losing in FIFA was clearly good indicator for them to stop this all, but they are not accepting this and now going at next level.
Court of Arbitration maybe more powerful. But why should they side with Chile?