I don't think any diet can fix a bingeing problem. You may want to check out the chicks in control section for some support with that.
I've done both Nutrisystem and Medifast, so I can tell you about my experience with them.
I did a Nutrisystem weekends off plan a few years ago. Weight loss was VERY slow, and I got frustrated after just a few months. It turned out to be very expensive also, because I had to add fruit, vegetables, and dairy to every meal, plus all the meals for the weekend. I also got so sick of their food - I literally was counting the days til the weekend when I could cook some real food.
I've been doing Medifast since April, and this is the most weight I've ever lost. I'm still motivated to keep going, too. Yes, there is still a lot of packaged food, but I get to eat 1 meal of real food EVERY DAY. I've adapted some of my favorite recipes to fit Medifast requirements, and I'm having fun trying new recipes. Yes, it's expensive too, but cheaper than Nutrisystem in the end. I eat out at least once a week on Medifast, so I don't feel deprived in that department.
Good luck with whatever you decide.
Lost the first 100 with Medifast, now working on the last 25