I'm a poli sci major who's taken a good chunk of Classics and History classes (although no Greek or Latin), for whatever that's worth.
My overall impression of the Classics department is that's it's rather close and tight-knit (by nature of it being a small department); many of the students are in multiple classes together and will have the same professors for multiple classes. The handful of classics majors I know are all great kids and have a lot of fun, but they're also pretty busy (but who isn't at NU?).
The history department, on the other hand, is much larger and there's quite a range of students in there. You'll find some truly passionate history majors, but there's also a large group who are history majors simply for a lack of anything better to do (something you'll definitely see in political science as well). The professors are all just as competent, but some might be a little less accessible, simply because they have so many students to contend with.
One thing you might want to consider is whether or not your interest in classics (or history for that matter) is strong enough to warrant a second major. Minoring in Classics or History is possible, and you could even potentially major in political science and get two minors in both. Also, certain Classics classes can be used to fill several of your distros (Historical studies (IV), Ethics and Values (V), and Literature and Fine Arts (VI) I think). Lots of History classes will naturally fill IV as well, and the related-courses part of the political science major could allow you to count a number of History classes towards your degree.
Bottom line: in both departments, you'll get out whatever you put in, although the size of the Classics department might make it a little more accessible; also, don't forget minoring options, including a major with a double minor; finally, you don't have to decide for a while if you're not sure, and the structure of the political science major means that you can take classes in Classics or History that will still count toward your degree even if you ultimately don't major or minor in that department.