Read about it here http://www.eecs.berkeley.edu/Programs/two_ways.html
Far and away the most important difference is when and how you get admitted. EECS students (in the College of Engineering) are directly admitted as freshmen, and need a 2.0 GPA to successfully graduate with their degree. Those who want to study CS in the College of Letters and Science have to complete all the lower-division CS coursework in their fresh and soph years and then apply to declare the major. Depending on your grades, there is the significant chance that you will not be allowed to declare the major and hence you will have to major in something else. Hence, you run the significant risk that you will take all the lower-division coursework only to find out later that you can't declare the major.
Here are the 'admissions' stats for those people who tried to get into the CS major in L&S. You will notice that a significant number of people did not make it. http://www.eecs.berkeley.edu/Peer/lo...tatistics.html
Hence, EECS in the College of Engineering is clearly a far safer choice. All you have to do is successfully graduate. With the L&S road, you're only told in your junior year whether you will be allowed into the major or not. Maybe you will, maybe you won't. You don't know.
On the other hand, it is significantly more difficult to get into Berkeley as an EECS applicant than as a L&S applicant. And you can only send one application to Berkeley. Hence, applying as EECS means that you run the increased risk of not getting into Berkeley at all. If you apply to L&S, then you increase your chances of getting into Berkeley in some capacity, but you may find later that you won't be allowed to declare CS. Hence, it's a tradeoff. A more difficult shot in the beginning (but if you make it, then more assurance of your major in the future) vs. an easier shot in the beginning, but more uncertainty of your major down the line.