A BS is a Bachelor of Science, a BA is a Bachelor of Arts, and a BGS is a Bachelor of General Studies. Although the same number of credit hours is required to complete each degree, there are differences in what courses can be used to fill those credit hours.
Each type of bachelor's degree has different "general requirements" that must be fulfilled to receive the degree. These requirements are fulfilled by taking courses in specific areas. The BS requires a certain number of math and science courses. The BA requires a certain number of art, humanities and foreign language courses. Both the BS and BA degrees usually require the student to declare a particular major, which will have its own set of requirements above and beyond the general requirements.
By contrast, the BGS often does not require a specific major, and the requirements can be satisfied by a wider range of courses. Many colleges offer a BGS to students with previous college credit in order to smooth the transition to a different institution. At the University of Connecticut, for example, the BGS is geared toward continuing students who have already completed an Associate degree elsewhere.
If the student isn't sure of a specific major and/or is interested in a wide variety of subjects, a BGS will offer a broader range of classes to choose from over the course of her academic career. However, if a student knows she wants a career in a particular field, choosing to pursue a BS or BA may be better for her--not only academically, by learning more about her chosen subjects, but by giving a potential edge over other applicants in the job market.
While the BGS is equal to the BS and BA in the sense that degree-awarded students complete the same number of credit hours, some employers may be skeptical of the BGS due to its unfamiliarity. For jobs that require an applicant to prove he hass studied the field sufficiently, job applicants with a BGS may be at a disadvantage compared to job applicants who majored in that subject area.
Graduate schools look at far more than the letters indicating an applicant's degree. Admissions officers will examine overall GPA, the specific courses taken and how many upper-division courses were taken, as well as letters of recommendation, personal essays and GRE scores. As long as the applicant is qualified for the graduate program to which she's applying, she should be on an equal footing with her BS or BA counterparts.