I wouldn't worry about your degree at all, no matter what it is. I've noticed a SLIGHT advantage for hard-science majors, but I think that's only because... and I'm not trying to stir up any fights here... because they're accustomed to having a more difficult course load than humanities majors are used to. Still, one of the top-most ranked students in my section was a philosophy major. People from ALL walks of life stumble into law school, and where exactly they came from doesn't seem to matter as much as you might think.
At the end of the day, in today's environment of grade inflation and slipping standards, a Bachelor's Degree is a glorified high school diploma. We all had more or less the same core classes... don't think that having four or so semesters of material that was different from the person sitting next to means that your brain is hard-wired differently for life.