The degree title won’t hold you back–they will look at the coursework and what you have done.
The differences between a BA and BS vary WIDELY. A lot of people seem to assume a BS means harder coursework but it’s completely school-dependent. I have worked at both private and public research universities and the only difference between BA and BS science degrees at all of these was that the BA required four semesters of a world language and the BS had four open elective slots that could come from any subject. The math and science requirements were exactly the same otherwise.