I'd say go for it if you think you've got a shot at MBB or top tier boutique. Management consulting is the most well-marketed exit opp for bschool grads, but there are a lot of mixed feelings within the industry itself (prestige aside). At worst you make 80-90k/year, and MBB really closes no doors.
Oh, and speaking from my own experiences with medicine and consulting - the grass is always greener. Try to think critically about what consultants actually do and whether or not you would really like it. The travel isn't real travel (what? you think we go anywhere except client site and our hotel +/- a restaurant now and then?) and you get real tired of living out of suitcase 4 days a week, even if your meals and taxis are expensed. The work itself leaves much to be desired; it's marketed as "high-exposure" and "diverse" and to be fair it is. But ask yourself if you think 3-6 months is really enough to fully understand an industry. It's difficult work but in large part only because you will constantly lag behind the learning curve at every engagement. Your team is constantly switching (and if you're with McKinsey they won't even be from your office due to global staffing) so you have no real work friends. Oh and did I mention global staffing really sucks?
There's a funny theory one of my colleagues and I made up which is that the best and brightest consultants always leave the firm for startups and upper corporate management, being fed up with consulting life. The weakest are culled after 2nd year, leaving only the mediocre or prestige-obsessed to spend their lives on partner track.
I'm being one-sided, but I think consulting does a fine enough job of selling itself. It's not all bad - the prestige is great and people really do notice. But if that's all you're looking for then medicine will bring you the exact same thing.
EDIT: realized you had actual questions.
1). doesn't consulting pay better than medicine, at least in the short run? Does that equalize out in the long run?
Depends on what you exit into. Entry pay at MBB and some top tier boutique is 70 + 5k signing + bonus = 85-90k/year. At senior consultant (>2 years) you will be breaking 100k with 20k bonus. I know a guy at BCG in his 3rd year making 150k/year. The opportunity cost of med school (4 years) is around 500k, plus 300k actual debt. We'll round off to $1m if we count residency.
There's no question of which is better paying if were talking MBB. Alumni at lower tier firms would probably even out with Dr's in competitive residencies after around 10 years.
2) Is the saying that "if you can see yourself doing anything other than be a doctor, don't be a doctor" true?
No that's just dumb. I mean, that's even assuming that doctors all do the same thing.
3) Is it also true that most people, on their way to becoming doctors, lose that compassion/burn out? Is this an even greater risk if you were never burning to become a doctor?
People who burn out in med school would burn out in consulting. I have no doubt of this.
All in all: I would suggest med school if you can't get into MBB out of undergrad. Your brand will probably get you interviews at these firms if you have decent grades and leadership but you still need to crack the case.