The Website of Jeremy D. Frens
Advising
I've talked with some of my colleagues at Calvin and two of my professors from Indiana University. One of the professors at Indiana University was, at the time, in charge of graduate admissions for the Computer Science Department.
I have not talked to anyone in industry about the differences between a B.A. and a B.C.S.
A B.A. is considered a broad education; you have a good deal of computer knowledge, but you've been educated in other areas giving you a well rounded education.
A B.C.S. is a more focused education; you might have a little more Computer Science knowledge, you will have a lot math, you will have a lot of science courses. You'll have a lot of depth knowledge in the sciences.
The graduate school people I've talked to say that which degree you get really doesn't matter. Perhaps at one time the thinking was that a B.A. teaches people to think which is crucial for further study and research (the goals of graduate school). But a B.C.S. says that you can work really hard to pass some rather tough courses. This can also be a good indication of how well you'll do in graduate school.
Your numbers (e.g., GPA and GRE), not the name of your degree, will get you to the top of the admission piles; your personal statement and letters of recommendation put your over the top and in.
The types of courses you take may also matter, but this cuts both ways. Some might be impressed with lots of hard math and science courses (like you get with a B.C.S.); others like to see breadth (like what you get with a B.A.).
Keep in mind that many computer science programs will accept people with non-computer-science degrees. Some schools are happy to take you if you know just enough computer science so that you're not embarrassing. I knew several students in graduate school (in the early 1990s) who did not have computer science degrees. It's not necessarily what you know, but how well you know what you do know.
See my graduate school page for more information.
Having never talked to anyone in industry, I'm not sure of the real perspective here. I can't imagine that it's much different than the graduate school perspective above. A B.C.S. does pose a bigger challenge, so that might add some points to your various numbers, but it's a risk because there can be more work which makes it harder to get good base numbers. That is, a good GPA with a B.A. is better than a weak GPA with a B.C.S.