Master's at Undergrad University Then Pursue PhD Elsewhere
My answer reflects the situation in the US and Canada.  In the US, most Ph.D. programs accept people directly from undergrad; at a few US and most Canadian schools you'll be expected to start in a master's program, but it is generally relatively easy to move up to the Ph.D. program (not significantly harder than avoiding getting kicked out of most US Ph.D. programs).  Whether it says "MS" on your degree will matter less than what courses you have taken.  Having another year of coursework will probably strengthen your application (or at least gives you a chance to), but if you have to pay a significant amount of tuition, then I have serious concerns about whether it will be worth it. If you can get into a funded master's or Ph.D. program, then that will save you a LOT of money, and you can get roughly the same boost to your future applications spending a year there that you would by being in the BS/MS program.

EDIT:  Since the OP has clarified that the extra year would be funded with a stipend, my comments above aren't really applicable.  In that case, it probably is the best plan to stay at the current university and get the BS/MS.  

Maybe I'll just make a general comment here which seems relevant: its generally pretty advantageous to stay longer at the current stage of career where you already are, as opposed to moving on in a rush.  Our culture makes a powerful mystique around completing things quickly, but all other things being equal, it is to your benefit to be a little ahead in actual accomplishments of where you are in your career (which extra time is one way of accomplishing).  You get "clock resets" at various points of your career (when starting or finishing a Ph.D., for example), if you can get more done before those, all the better.  Of course, often financial or personal considerations have to be weighed against this.