If you are just going to drink it once, there is no difference.
If you are going to drink them habitually then we need to know more about the contexts in which you drink them, how often, etc. If you were to only drink one per week for example and you are otherwise living a healthy life, then probably you would find something like “they are about dead even but maybe the Coke is ever so slightly healthier?”—this sort of thing gets dominated by the really little things like some people have phenylketonuria which means they shouldn’t consume proteins containing the amino acid phenylalanine, and aspartame is a really simple protein (only two amino acids, I think?) containing phenylalanine.
On the flip side, if you drink a lot of Coke or fruit juice, each dose is giving you about as much calories as a glass of beer or wine and a similar analysis results; a bunch of those calories in both cases need to be processed by your liver and your liver can get overworked and even if it doesn’t get overworked you are likely not hitting the gym once for each sugary drink and so the surplus energy increases your equilibrium weight until you start burning the extra calories by merely existing.
By contrast the research on artificial sweeteners tends to not show negative effects here. There are some potential risks; I know a guy who is very DIY-health-ish who used to taste his urine because of some prediabetic condition where he would pee out sugars; he said that he would never drink Diet Coke again because it made his urine taste sweet (most of it passed through unharmed) but unnaturally foul (some of the aspartame was getting converted into something really nasty).
But the key thing is that most artificial sweeteners are thousands or tens of thousands of times more sweet than sugar, so there's actually surprisingly few molecules in the drink that are artificial, so you tend to get an unusually low dose of any toxicity. This is also why artificial sweeteners have a huge problem matching the natural taste of sugar—amplification of a weak signal always makes it really hard to replicate a target signal.