IMHO, you can lose faster on Atkins compared to a *normal low-fat diet*, but not Medifast.
I have been on Atkins, have lost weight on it, yes, but 1-2 pounds a week, not the 3 I average with Medifast. Plus while I love bacon, meat and cheese, I actually have more energy on the MF. But that's me...
But I would say across the board because MF is dramatically low in calories, most people will lose faster on it than on Atkins.
I mean, in my experience, you should choose what YOU feel most comfortable with. If she wants to do Atkins, hey, more power to her! I think if done properly (with a big salad/veggies every day! And no porking out on the cheese! Heh!), that it can be a healthy way to lose weight and remarkably, to improve cholesterol and other problems.
It definitely stabilized my blood sugar! And the protein in it keeps people full longer and they eat less food = weight loss. Plus I read a theory that there is a 300 daily calorie 'allowance' on Atkins - that is to say, if Dieter A eats 1500 calories of low-fat foods, they'll lose 2 pounds a week. But Dieter B on Atkins can eat 1800 calories, lose the same... because the fat/proteins require more energy to digest. So the theory goes
(I just gave a rough example, but the added buffer in the study was 300 calories.)
I found that there can be a lot of variety on Atkins... there are several good low-carb cookbooks out there, esp. by Dana Carpender.
Pitfalls of Atkins: hmm...
1) If done incorrectly, without enough focus on keeping greens in the plan, you can get tremendously constipated. I mean, for days and days.
2) It can be expensive to buy meats/cheese/seafood, etc, especially if you are trying to go organic beef, etc. (But really, maybe cheaper than MF, so this is kinda a red-herring non-issue.)
3) Your breath can get super stinky from ketosis.
4) It could lead to people going carb-crazy from withdrawal if they stay on Induction too long... and if they go on a carb fest regularly and cycle back and forth between Atkins/carb-loading, that is The Best Way Ever to get really, really fat. Trust me, I know.
5) Gotta watch salt on it if you are sensitive and eat a lot of processed meats - bacon, hot dogs, deli meats. Your salt intake can go through the roof and you don't notice until your ankles look like the Michelin Man (again, I know all about this. Shoulda known better!)
But really, in my opinion, no big pitfalls on Atkins. Just a personal decision for each person, I say... I'll take my 3 pounds a week though and non-stinky breath!