That is the hope.....
The reality is that both CEOs probably do the same. If one happens to do better than the other, he will use it to justify a higher compensation.
American CEOs are paid significantly higher than their international counterparts. American companies do not perform significantly better.
Neither do workers, probably even less so.
People have value, and nobody is going to pay somebody of little value a lot of money. They have to have value in some capacity. Conversely, nobody is going to overpay a worker either in most cases. CEO's, especially the best ones, are very rare; just as rare as that star quarterback, ace pitcher, beautiful and talented actress, or the great song writer. Because they are rare, they can make higher demands for compensation, because if you don't want to meet those demands, somebody else just might, and then those people get the talent.
In other words, take your job for instance. What if only you and a handful of people had the ability to do your job? What kind of money would you make? Well.....as long as you could produce profit for a company, you might be able to ask for millions a year, and companies would have no choice but to take it.