Superpolynomial Simulator One method for proving a protocol secure is through simulation-based models. This simulator uses ideal/real paradigm in which a protocol is secure in the real model if it is proven secure in an ideal model using a trusted third party (you can refer to the Canetti's UC framework to realize what is the power and use of this simulator, although use of this simulator dates back to 80s). This simulator is often given polynomial power to simulate the ideal world and if an external entity (observer) cannot distinguish between a real run and a simulated run with probability at most half plus negligible, we say that the protocol is secure or following UC terminology for realizing a functionality, the protocol securely realizes the functionality. It is good to mention that the simulator is also simulating the attacker, so the power of the simulator is essentially power of the attacker. There is often times that the simulator has superpolynomial power.


  Question: Does superpolynomial simulator has any advantage over a polynomial simulator? I need a good article on cons and pros of such a simulator.


A good article in which the author have used a polynomial simulator is Adaptive Hardness and Composable Security in the Plain Model from Standard Assumptions of Canetti.
Well, your edited version of the question revealed a reference to the following paper:

Rafael Pass. 2003. Simulation in quasi-polynomial time, and its application to protocol composition. In Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques (EUROCRYPT'03), Eli Biham (Ed.). Springer-Verlag, Berlin, Heidelberg, 160-176. (See also this version.)

The paper discusses and justifies the need for such simulators. 
The abstract reads:


  We propose a relaxation of zero-knowledge, by allowing the
  simulator to run in quasi-polynomial time. We show that protocols satisfying this notion can be constructed in settings where the standard definition is too restrictive. Specifically, we construct constant-round straight-line concurrent quasi-polynomial time simulatable arguments and show
  that such arguments can be used in advanced composition operations without any set-up assumptions. Our protocols rely on slightly strong,
  but standard type assumptions (namely the existence of one-to-one one-way functions secure against subexponential circuits).


For a more thorough discussion, I suggest taking a look at Rafael Pass's M.Sc. thesis.