I quit drinking diet soda (i.e. Pepsi Max) some weeks ago, along with all sugar free juices, concentrates, and anything else artificially sweetened. I chose to go cold turkey with no replacements, knowing that if I get a craving for something, I can get flavoured water (unsweetened) or make ice tea. I used to gulp down a 1.5 L bottle every day.
I don't notice much difference, aside from the slight bouts of headache I got the first few days when I slashed my caffeine intake. I have had some heartburn, stomach and digestion issues lately, but in addition to removing all sweeteners, I stopped buying processed foods and quit smoking, which I think was a shock to the system.
One earlier experience I remember, I quit diet soda for half a year months back in mid-2000. Then I lost 3 lbs the first week when a lot of swelling the soda had caused disappeared. And it was the same Pepsi Max, not sugary stuff.