Community college AA History graduate here going to university soon and I'm debating between a BA in History and BS in History with a concentration in "Applied & Public History". The BS is at a different school so I'd need to make a choice before transferring. I'm aiming for archival or museum work eventually but I’m not picky. Looking for advice.
If you want to do museum work or some other type of public history, I would advise you to do the B.S. in history with the applied and public history concentration. If you are interested in traditional academic history, especially someday a PhD program, do the traditional B.A. degree. Sometimes there is not a lot of difference between a B.A. and a B.S., but most of the time the distinction is that a B.A. requires substantial foreign language coursework, as Eistean notes. It might seem like skipping the foreign language is a good idea, but that would actually be a mistake if you want to go on to a graduate degree. Graduate programs generally require reading proficiency in multiple languages for any field except American history, and many require at least one even for Americanists.
Don't pay too much attention to the BA vs BS designations. Look at the courses you'd be taking, look at the backgrounds of the professors.
I got a BS in History instead of a BA. With the BS all I had to take was a statistics course. With a BA I would have had to take four foreign language classes. So I was able to use the other three courses in classes that advanced my career more (American Art, Marketing, Parks and Rec, and so forth).
I can't tell you about how it works in higher academia, but in the museum field it often really doesn't matter at all, especially so long as you have an MA. Also the obligatory: Feel free to join us at /r/MuseumPros!