What is the big advantages of ASP.NET MVC over ASP.NET Web Forms?

1- Separte Views ( UI ) - Controllers (Bussiness logic) Models (data storge)

2- Mantaince - unit test

3- menimum code writen

Each can be the “best choice” for a particular solution depending on the requirements of the application and the background of the team members involved. What to choose and when has more to do with business prospective than which one is better than other. When facing a decision to choose between ASP.NET Web Forms or ASP.NET MVC it is important to know that neither technology is meant to replace the other.

Two important factors you should consider while making the choice is

1. Rapid application development - If you want to develop anything rapidly ASP.NET Web Forms is the only chance you are having, you can’t even consider for ASP.NET MVC for RAD.  (Reasons for RAD may be anything like client is not paying too much, or application is going to be used for only one or two months and won’t require much maintenance.)
2. Unit Testing - If automatic unit testing is most important factor for you MVC will be best for you.

Other than these, what you can do is, write down all your project requirement and try to compare them with Pros and Cons of both Web Forms and MVC and if possible try to ask yourself following questions and point MVC and Web Forms accordingly

1. Does your team have good experience with Web Forms or Windows Forms?Well, if yes then probably learning ASP.NET MVC is going to be a tedious task for team, because developers have been used to with ViewState and event driven programming by now and migration is going to be a difficult task.1 point to Web Forms.
2. Does your team have good experience with ASP.NET MVC?If yes ASP.NET MVC get1 point 
3. Does your team have experience on ASP or non-Microsoft technologies such as android, ios, JSP, ROR, PHP?If you have been JSP or ASP developer prior then you might be familiar with HTTP get and Post and even u might have hands on with MVC because most of them use MVC by default. It gives1 point to ASP.NET MVC.
4. Is JavaScript going to be used extensively?If Yes, MVC gets the point because you get complete control over HTML.1 point ASP.NET MVC. 
5. Looking for good performance?With no support for ViewState ASP.NET MVC provides good performance gain over traditional ASP.NET Web Forms.1 point ASP.NET MVC. 
6. Planning to reuse the same input logic?If yes stick with MVC.

Hope this helps.

If you are looking to develop something fast regardless of code quality, web forms is your choice. But if you want to develop something based on international standards and third party libraries with a clean and easy to understand code, MVC is your best choice. Moreover, ASP.NET Web forms uses the control state property which adds a huge chunck of code in the view ths affecting web site loading time unlike MVC based on javascript and jQuery.

MVC provides the ability to separte the View (i.e. the UI) from the bussiness logic. That way the bussiness logic can be independently unit tested. The View also becomes very thin (i.e. with minimum code) which is good because it is hard to unit test the View.

MVC minimize your code as comapred to it's compartive techique3 tier

MVC is based upon Seperation of Concerns Principal where the architecture force us to think in terms of business logic and underlying datastore seperately. One thing which is very important is that MVC is not a new concept it has been there for years, so what prompts Microsoft to adopt this concept should be enough reason for the .net developers to follow the suite

some advantages for MVC over  Webform for example there is no view state , you can use more than form ,highly integrated with Microsoft EF 

MVC is the real way of web lifecycle. Web forms is a whole library that enables web development to look like a windows project. But MVC works in pipeline logic. If you develop a MVC project you can see the progress clearly (server side and client side). There are some data transfer between server and client and that is all.

Also in MVC you have the all control of generated html, so it is faster and efficient.

The main advantages of ASP.net MVC are: Enables the full control over the rendered HTML. Provides clean separation of concerns(SoC). Enables Test Driven Development (TDD)

i Think the biggest advantage is Software enginnering Principle

 Separation of concerns (SoC) and Test Driven Development (TDD) With MVC, you can more easily create tests for the web side of things

one of the biggest advantage is seperation of concern i.e. the seperation of logic from the view using controller to map the views to the data (model). this maes readabilty easier and also future modification of the code. unlike code behind approach all the logic liew in the controller and all the data calls in model while the view is strictly the template that uses the model data to show mwaningful information on screen.