From what I have read, course specific GPA, recommendations, and GRE scores are some of the most important factors when it comes to acceptance into grad school. A B.A. may be more preffered if you are planning to switch from (using your example) physics to c.s./engineering since the coursework is less concentrated in physics and is more spread out upon engineering science, chemistry, and the such (or atleast this is the B.A. program at Cleveland State University).
However, it is important to note that you could get a bachelors in philosophy and still be able to get accepted into a masters program of engineering. If you have enough experience and you can prove it you could also get accepted into a masters program with no degree. So, in short the degree you receive as an undergrad does not have a significant effect on the ability to get a masters degree. However, many universities do prefer that a candidate has an undergraduate degree.