If you want to make an impact on an important problem, I'd focus on the advisor first, not the area of research. Pick an advisor with a track record for strong publications in quality journals. Someone who produces quality research will typically have the best sense of what problems are and aren't important, and can guide you much better than bystanders who don't know your skills. In addition, a strong advisor will have the contacts necessary to get you in touch with other top researchers in your field, which is extremely important in producing high quality publications.
The one with lots of publications in big-deal journals may or may not be running a sweatshop. And they may or may not be doing actually interesting science, because that game requires so much attention to fashion, fundability and grinding out large quantities of papers (contrary to common belief, prestigious journals do not mean journals publishing the highest quality papers).
But if you want to learn that particular trade then find the advisor best at it to study under.
