var myFunction = (...args) => {
  console.log(args)
  console.log(this)
}

is equal to

var myFunction = (function() {
  var args = Array.prototype.slice.call(arguments)
  console.log(args)
  console.log(this)
}).bind(this)

.bind makes the use of var self = this unnecessary.

From MDN:

An arrow function expression has a shorter syntax compared to function expressions and does not bind its own this, arguments, super, or new.target. Arrow functions are always anonymous. These function expressions are best suited for non-method functions and they can not be used as constructors.

This text explains everything Arrow Functions are and can do. So yes, there is more than just the this value, but no, they are mainly syntactical sugar for situations, where you just need a small handler as argument.