I'm studying CSE in a university and am currently at the end of my 2nd year. I'm having doubts on what to do in the summer: A project under a professor or develop my own games at home. I'm quiet a self started and like to do things on my own, but most of the people around me have been telling me that a project under a professor will be of much more value than a hobbie project done on your own. The question is quiet simple: what would a game development company value more while recruiting : a hobbie game project done on your own or a project under the guidance of a professor?

The answer to your classic two-choices question is "probably neither."
Unless a project you make is of high quality and demonstrates an elegant solution to a problem, it shouldn't go into your portfolio.
Don't think so much about what a game company might think about the project -- think for now about mastering the skills you need to master. Which one will do that better?

Do you have any interest in the work you would doing under your professor? If no, then I would probably lean towards the hobby project, because, for me, its hard to do something well if your not interested in it.

As for your hobby project, a big part of the value you would get from that is, if you had someone who could guide you and comment on your work. Its great to work on your own the project and it shows interest in what you want to do, but even if you produce something that works, you may have gone about it the wrong way and you'd want someone to tell you that. This is something that your professor would do under his project.