As my name suggests, I work for McKinsey. My perspective is also applicable to BCG (and somewhat less so to Bain).
Travel varies significantly by office and the type of work you do. Some consultants travel 4 days a week and others don't travel at all. I work far fewer hours than your typical resident, but I've spent about 4-5 months of my time working in London, Paris, Berlin and Zurich. Yes, I travel, but I'm definitely not complaining.
The average time someone spends my firm is about 2-3 years. But if you're interested in partnership and the potential to make a seven figure salary, it takes about 6 years (e.g. the same amount of time going from intern year through the end of a medicine fellowship).
Someone mentioned doing residency earlier in the thread. The long-term economic argument is just not there given the options outside of clinical medicine. This is on top of a huge short term earning gap during the resident's 3-10 year training period. So it should come down to how you see your future career playing out: residency is appropriate if you want to reserve the right to practice medicine in the future. But it's wrong to say that residency as "professional experience" would help you settle into a career in finance (VC, PE) or management in a healthcare company. Spending 2-6 years at a top consultancy would do far more for you.