Classmates can only compete among themselves. Sometimes they can help, but it's very rare. It is this rivalry that stimulates them to improve their knowledge. But teachers have more knowledge and they can more effectively teach.
Perhaps if you're in physical classroom. But if you look for example courses on edx or coursera, you can see that peers motivate each other (especially if there's facebook group or some kind of forum) and I didn't see a competition per se but pure encouragement and students helping each other.
I think its a broad assumption and it depends upon the situation. peers really inspire us to learn and even to learn some naughtiness. Some peers are bad influence too. That is why it is good to be surrounded by good people, good peers or groups.