From a fat loss perspective, you're far better off with diet soda than regular soda because the former is calorie-free and the latter is calorie dense and liquid calories are notorious for sabotaging fat loss.
This has been researched extensively including randomized controlled trials.
For example, it should be common sense, that 200 calories in a soda vs 0 calories in a diet soda should be a no brainer that swapping a regular coke for a Diet Coke will improve fat loss.
But many people have strange ideas about diet soda and artificial sweeteners that are not scientifically accurate.
The only potential issue on the fat loss side is that its possible that when people drink diet drinks they subconsciously or consciously see that as permission to consume more calories elsewhere.
From the health viewpoint, there's very little reason to fear any health consequences.
Artificial sweeteners have been studied for safety probably more than any other consumable substance in history.
Still people fear it, but there is no scientific reason why.
Now the downside is that diet soda provides zero nutritional value.
That being said, there are better optoms. If you drank tea or yes even black coffee, you would get loads of healthful compounds like antioxidants and virtually no calories.