The Mishna doesn't mean to say that this world is greater than the world to come because as we explained last week the entire purpose of this world is only to allow us to attain the eternal reward of the world to come. The point of the Mishna is though that as long as we are still alive in this world we have the opportunity to engage in Torah and good deeds which will perfect us and allow us to attain the reward of the world to come. Once a person dies they no longer have the opportunity to perform good deeds and perfect themselves, whatever they accomplished in this world is what they are left with for eternity. This is what our Sages say King Solomon was alluding to when he said "the living dog is greater than the dead lion". The lowly dog has a great advantage over the mighty lion if the dog is alive while the lion is dead. The reason is that the dog can still accomplish and perfect himself whereas the lion can no longer progress through his actions.