Should I switch from an M.A. to an M.S. program if my department allows me to choose? I work in industry and am also attending a major U.S. university to get another master's degree, this one in Applied Math. 

When I entered the program, the department offered a Master of Arts (M.A.) degree for Applied Math. This year, the department made a change to Master of Science (M.S.); any new students coming in Fall 2014 will be M.S. students, and any current students will be given the option of switching their degree from M.A. to M.S.

Should I make the switch from M.A. to M.S.? I already have a M.S. degree in engineering. In my opinion, all other things equal, M.S. is considered more rigorous from an employer's perspective.
In general, I believe your assessment is correct—for scientific disciplines where both an MA and MS are possible, the MS degree is usually regarded as more rigorous than the corresponding MA degree.

That said, whether you should switch is a matter that requires some thought. Does the change require you to complete more courses? Will there be any impact on your expected graduation date, and the cost of getting the degree? If not, then I would definitely switch. (Moreover, since you already have an MS in engineering, there's no point in getting an MA afterwards. If you didn't have a master's, you'd need to figure out the relative advantage of finishing faster versus the more rigorous degree.)