Both schools are excellent for premed with superb counseling (that offer committee letters when applying to medical school), small class size, attentive faculty, and great opportunities for research. Hopkins has a wider breadth of STEM research going on if you’re interested in pursuing research (which isn’t necessary for medical school but a common activity for applicants).
I think you’re splitting hairs here when it come to pre-med benefits at these schools. The biggest difference you would encounter is that more students at Hopkins will be on a premed track (often 15-25%). I’m guessing the “pressure cooker” comment was referencing this fact. This can lead to competition (note: not cutthroat) in coursework. Some people like being surrounded by others in the same boat since it provides them support and drive, others find it overwhelming. Depends on who you are.
More importantly, I would consider the atmosphere you want to study in for four years. Have you visited both schools? Hopkins is in a residential community a few miles north of a large urban city while Princeton is further removed in a small college town with a suburban feel. If you’re interested in public health and working with minority populations and socioeconomic disparities then I would recommend studying at Hopkins since the school offers many opportunities for outreach in a variety of settings.