Wooldridge's Microeconomics book vs Cameron and Trivedi's textbook
Both books are very good, and they are not competitive but rather complementary. I would say that compared to $CT$, $W$ is a more "traditional" econometrics book, while $CT$ includes whole chapters in broader underlying statistical issues. At the same time, $CT$  are relatively more concerned with the dirty reality of doing applied econometrics with real-world data sets, and how this feeds back to the theoretical models. 

Regarding your choice, it matters what each instructor does with each book. Ask them.

Learn which chapters are covered in each class and compare, to see if they cover the same subjects or not... there must be a reason why there exist two available classes.