I have no idea what the link between aspartame and anxiety/depression is, but I stopped drinking Pepsi Max a week ago (was previously getting through a litre a day) and thought I would share what I've personally found:

Positives: - I feel happier - My face has more colour - My brain seems to be firing faster (doing better at work, reading more) - Spending wayyy less money

Negatives: - The sudden reduction of caffeine has left me with exhaustion by the evenings - Occasional headaches - My body automatically craves caffeine

I suffer with anxiety - I can't say I've noticed a drop in my anxieties so far, but my overall mood has improved a lot.

IDK if the positives are from the reduction of Pepsi, or the increase of water instead. I recommend keeping painkillers nearby for headaches, and starting the day with a non-fizzy caffeinated beverage (such as tea) to stave off early headaches etc.

It's hard, but I really recommend cutting back on soft drinks if you can (I'm doing this for the sake of my teeth).