What are the pros and cons of doing PhD study at a big vs. small department?
The main disadvantage of being a student in a big department is that the professor can not actually provide in-depth mentorship to that many people: your "real" advisor will most likely be some post-doc instead. The quality of post-doc advice is more variable since they haven't had as long as a professor to prove and improve themselves. (This one bit me personally, and I switched from a largeish department to a small one where I like it much better.)

On the plus side, a big team will likely have several different funding sources, so if your main grant runs out but you don't have enough work to graduate yet, it'll be easier to find you another contract to tide you over.