Let me compare the two for you:
Asp.net web forms
They matured the old ASP technology that was much more like PHP. Code and presentation were piled up in the same file. Asp.net web forms upgraded this model by providing a mechanism of separating the two. But they built on top of the good things that windows application developers had. The drag drop interface creation with control events just like they exist in a windows application.
Therefore it was rather easy to start developing on Asp.net web forms. But non savvy developers soon got to a bottleneck they didn't know existed (like slow postbacks due to huge view state etc.). Technology used some tricks to make this work. But on a serious large scale application this became quite a problem. Developers had to mingle their code to make it work with Asp.net web forms framework. Their complex forms had complex codebehinds with hard maintainable code with complex state.
The good (as well the bad) thing were at that time rich server cotnrols. Nowadays with web 2.0 they don't seem rich anymore since they don't actually support client side functionality as much as they should. So Microsoft decided to also cram in something else. Update panels. That made partial rendering (and Ajax) possible with almost a flick of a finger. But it came with a cost. Everyone that used (uses) it soon realised it's not a viable solution that a professional application could implement.
Asp.net MVC
Now we have a new technology that doesn't have much in common with Asp.net web forms except for its first part of the name. MVC framework actually does separate code from user interface (view). Controller actions (code that executes on any HTTP request) is kept small and doesn't do anything with visualisation (it doesn't bind data to certain controls etc.). Controller action barely prepares data for the view to either consume or not. It's up to the view.
Views on the other hand just display and provide data. They can be partially or fully rendered. They support Ajax functionality to the point that everyone would like to use. Actually everything is separated into basic little things. Divide et impera (divide and conquer) seems to be the save-line here.
There's not hidden functionality. No flirting with windows development. It pure request response framework. Developer has the ability to 100% control the visual aspect of their app. But for the cost of not having rich controls out of the box. Those may be provided by the community or some developers prefer to create per purpose controls that serve the process much better.
Which one is better then?
Both have their pros and cons. But if you decide to build a semi complex, modern and maintainable application I'd suggest you give MVC a go.
But if all you need to do is a 15 screens application (without any particular interface requirements) it would be much faster to create it using Asp.net web forms.