Personally, Aspartame and Splenda have no effect on me. A year ago, at the urging of several friends, I cut out artificial sugars. I did it cold turkey which, was a feat, in itself, considering I drank at least 4 cans and/or bottles plus a large fountain pop a day. Everyone swore it would make me feel so much better but, I found no change in how I felt. It would have been really nice to have a solid reason to not drink pop but nothing changed. A couple of weeks ago I started having the occasional pop and it didn't harm me. I never stopped missing the taste of diet coke so I am finding the occasional one helps me from slipping back into drinking it in excess.
Personally, I think they're like everything else. Some people are sensitive to them and others are not. Everyone needs to find out for themselves how it effects their system and go from there. I know some people are against using artificial sugars but, I'm not. If Aspartame is going to give me Cancer, I'll never know because I'm at risk for it to begin with.