Losing weight and changing our way of life and way of eating is a psychological battle as much as a physical one.
I, too, had trouble believing I could lose weight while enjoying a "normal" dinner every night, and even an occasional treat. But, I'm doing it!
It's true, though, that everybody's body is different and you have to do what works for you. All you can do is try it, if you feel you'd like to, and see what happens. You never know, you might even lose faster than you do on Atkins.
Having done Atkins once before, I find that I lose at almost the same rate when doing either Atkins or CAD and I have a much easier time staying on CAD.
But, you can only do what you're comfortable with (mentally and physically). I understand your fear of slowing your weight loss, so go with what you can handle.
Remember, if you're like me, you've carried lots of extra weight around for quite some time, so why the emergency now to lose weight FAST, FAST, FAST! Take comfort in the idea that you are doing something really good for your body and the weight loss will come. (I find that way of thinking much easier on CAD because I don't feel like I'm suffering or deprived.)
Good luck to you in your continued quest for ultimate health and well-being!