BSCS v BACS

I just got into the engineering school and was pre-selected for the comp sci major. However I want to double major in LSA and I know this is very difficult since I am in the engineering school. I was wondering how easy it is to switch to LSA because I know I can do comp sci in both schools. If I do switch am I still guaranteed to be able to major in comp sci in LSA? Also is there a difference between getting the BA or the BS in comp sci or not really.