Well, my situation was different but I got my bachelors in rather specific field - bioinorganic chemistry. Honestly we had 90% of the classes together with ppl who were getting their bachelors in other fields, namely bioorganic chemistry, general chemistry, applied chemistry and about 50% togerther with biochemistry undergrads.
There was almost no difference in knowledge after we got our degree. We few more clases in inorganic chemistry while they had more classes in biochemistry and molecular biology, but in the end all those classes were just introductory and we didnt delve deep enough. I have maybe better idea about coordination compounds or something else than my mates that get their Bc in other fields (while they obviously have better idea in other areas).
Anyway, I dont think that it realy matters, I value the general knowledge more than specifics but you might not. And I think that unless you are going to pursue PhD then its better to have more general idea than specifics that you might not even use in the future.
PS: Our school system is different than in the US, its 3 year bachelor, 2 years masters then PhD so we have more specific classes in the masters degree and almost no classes when pursuing PhD (well there are "clasess" but its more like self study and consultation than actual class)