Zipf's law is not only universal for city sizes, but also for city numbers; the number of cities in the first largest country is twice as many as that in the second largest country, three times as many as that in the third largest country, and so on.

https://www.researchgate.net/publication/260167281_Zipf's_Law_for_All_the_Natural_Cities_around_the_World

Article Zipf's Law for All the Natural Cities around the World

Everything is relative. Better for what?

There are many approaches. And more and more publications with different models.

See, for example, Alonso's "an aggregate theory of city size" in "The economics of urban size". Universal model (law) which takes into account ALL of relevant variables is more myth. Social systems (lile the cities) are not physical

Don't know about it being better than Zipf... yes, there is an alternative called Kleiber's law. 

 http://io9.com/the-mysterious-law-that-governs-the-size-of-your-city-1479244159

It might also be helpful to follow the literature on Urban Metabolism (UM). Such as:

https://www.researchgate.net/publication/281394483_Urban_Metabolism_A_Review_of_Current_Knowledge_and_Directions_for_Future_Study

Article Urban Metabolism: A Review of Current Knowledge and Directio...

Dear Hossein

You might be interested in these reflections on the matter, developed by Gabaix and Ioannides:

"The evolution of city size distributions", Handbook of Regional and Urban Economics

Volume 4, 2004, Pages 2341–2378

doi:10.1016/S1574-0080(04)80010-5

(The pdf of an earlier version of the text is also available on the webpage of one of the authors)

Best regards

d.

Dear Hossein Sadlounia 

Please see the following

journal homepage: www.elsevier.com/locate/cities

The city size distribution debate: Resolution for US urban regions and megalopolitan areas

Brian J.L. Berry ⇑, Adam Okulicz-Kozaryn

School of Economic, Political and Policy Sciences, The University of Texas at Dallas, 800 W. Campbell Road, GR31, Richardson, TX 75080-3021, United States

The case might seem to be closed, but at this juncture the recent literature has taken two critical turns. One group of scholars argues that an economic theory is not required because skewed distribution functions of the city size type are uniquely stochastic steady states. Another group has engaged in a confrontational debate about whether Gibrat’s Law describes urban growth and whether the size distribution is better classified as lognormal or Pareto. In the first group, Axtell and Florida (2001) have produced Zipfian steady states via agent-based modeling.10 Numerical solutions yield empirically-accurate firm characteristics: a right-skewed distribution of firm sizes, a double-exponential distribution of growth rates and variance in growth rates that decrease with size according to a power law, which in turn yield city-level macro behavior that satisfies Gibrat’s Law and produce the Zipf rank-size distribution as a steady state. In other words the result is self-organized complexity characterized by power law frequency-size scaling (Turcotte and Rundle, 2002). In the same vein, Semboloni (2001) has modeled multi-agent interactions via a probabilistic law to obtain opposing goals that conform to the Zipfian processes of unification and dispersion and used numerical analysis to reveal the circumstances under which the system converges on rank-size as a steady state. Gan et al. (2006) show via Monte Carlo simulation that the law is a statistical phenomenon that does not require an economic theory. Batty (2006) describes the rank-size distribution as emerging as the self-organized steady-state of a complex adaptive system (Batty, 2006), and Corominas-Murtra and Solé (2010) describe the law as a common statistical distribution displaying scaling behavior, an inevitable outcome of a general class of stochastic systems that evolve to a stable state somewhere between order and disorder.