I have read all the answers and feels my personal experience would add something to the answers above.
3-4 years back, I developed 2-3 website projects using Webforms. Around that time, MVC wasn't around or i didn't heard of it. The development was naturally(I was coming from Win-forms development with no prior web development experience) fast for me, since i need not to learn HTML in details and web-controls helped a lot (a hell lot, it made life easier).
Now, after all that time, i wasn't working any web project until recently and merely building some windows application using WPF.
Few days back I had an idea for a website and thought of developing it : this time around in MVC (since its talked about everywhere, besides i needed to learn either, so i choose MVC). The project is still in development phase, since i am still learning and building together.
So, the Key differences i find b/w the two are following :-
For someone coming from windows development, Web forms will always be favorable. Asp.net learning curve for a windows developer is bit steep
For someone coming from web development in some other technology, MVC will be favoured since it mocks the latest of them all.
Development is easier and cleaner in MVC if you are equipped with good knowledge of HTML and CSS
Deployment is still an issue. In web forms one just needed to do copy and paste. But, this requires some things to be done.
In short, both of them will stay here for a while.