Both schools offer a BA program in biology. Either program will do a fine job of preparing you for graduate or medical school.
The most obvious difference is that the biology department at SC is significantly larger than the one at BMC (about twice as many faculty). This should not be surprising, given that SC as a whole is significantly larger than BMC (about twice as many undergraduates). So if there is a particular biological subdiscipline or specialty that you are interested in, you might be more likely to find it at Smith.
On the other hand, Bryn Mawr cooperates closely with Haverford College, which is 10 minutes away by shuttle bus. BMC bio majors are free to take classes at HC; in fact, they can even major in biology at HC, rather than at BMC, if it seems like a better fit. The BMC/HC bio depts combined are about the same size as the SC bio dept.