I'm not sure about the aspartame withdrawals, but I do know that my mom gets terrible headaches when she withdrawals from caffeine and she doesn't ever use any artificial sweeteners. The last foot surgery she had where she couldn't have anything after midnight and the surgery got put off for a few hours so it ended up being after noon before she got out of there and she had a horrible headache and the doctor told her it was probably caffeine withdrawals.
I guess I'm stubborn, but I still have my diet sodas every day. I have heard all the horror stories about how bad the artificial sweeteners are, but there are poisons even in natural foods that we eat every day and I feel like we would have to eat a really significant amount for it to have any serious effects. That's only my opinion though. I listened to a diet doctor about 5-6 years ago who told me "If it hisses when you open it pretend it's a snake and stay away". Well I quit all carbonated beverages for over a year and it didn't make a bit of difference in how I felt or the weight I lost. I think it might be a trigger for some people and make them crave sweets, but it doesn't seem to be a trigger for me. I use the super potent ez sweetz drops (1 drop = 2 tsp sugar) in my coffee each morning and in my tea. I even cook with it. I have used it in recipes and brought them to work and even the people who say they can't stand artificial sweeteners said it didn't have an aftertaste. It's supposed to be liquid sucralose, some call it liquid splenda. I don't know what it is, but it tastes so much better than any other sweetener I have tried and I have tried a lot of them.
As far as withdrawals - I really don't remember if I had any headaches or anything back when I quit drinking carbonated beverages, but I never quit coffee or tea and back then I think I drank regular soda, not diet. It has been too long ago, so I can't remember for sure.
I was on the Atkins diet from July 2011 to October 2012 and I lost 73 pounds. October 15, 2012 started WW's and got down to 255. Gained 25 pounds through the holidays, but got back on track June 2013. Got off track through the holidays again and gained back 10+ pounds
I will continue my journey to the end, no matter how long that takes.