Before I get into it, I want to clarify that this is not an intelligence ranking. The best detective is not going to be the smartest member of the group and the worst detective is not going to be the dumbest member of the group. Detective skill does require significant intelligence, but all the members of the Chaotix are significantly intelligent.
In short, Ray is the smartest member of the team, hands down. He has more knowledge than anyone else, mostly ecological, geographical, and cultural knowledge, but he's brilliant. However, he's cowardly and doesn't perform well under pressure, so all those brains don't mean much when the team is in danger.
Contrarily, Charmy is the dumbest member of the team, simply because he's a 6 year old kid. Of course he's not going to be more intelligent than an 11 year old genius, two 16 year olds, and a 25 year old. He doesn't even know how to tell time yet, he's got a lot to learn and he certainly has a lot of growing up to do. Still, when it comes to detective skills, he's higher up than Ray because he is more experienced working cases and he has a knack for picking up on minor details that normal people might miss. Plus he keeps a level head in dangerous situations. (well, a relatively level head XDDD)
So without further ado, here's the hierarchy:
Vector is the best detective of the Chaotix, which is why he's the leader of the group. He has the most experience, the most knowledge of psychology, and the most attention to detail than anyone else, including a great memory to draw each and every clue possible out of. His hunches are second to none and he's just a logic machine. Vector is, hands down, the best.
Espio is great at gathering intelligence, but he doesn't always know what to do with the information. While he's clearly intelligent and understands people better than most, he's behind Vector in experience, psychology, and often misses the seemingly minor details. So he's the second best detective in the group, which is no small feat. He's right behind the best in the series and that's nothing to snuff at.
Charmy is actually a good detective and smarter than he looks. The problem is most of the time he isn't focused enough or he just doesn't care enough to actually use his deductive reasoning on his own. But once every blue moon, he'll use his full deductive powers to solve a problem. See Chapter 3 for a rare example of this. He's learning slowly but surely from the best every day and he's only 6 years old, so given time, he could very well be on Vector's level. But for now, he's well below Espio.
Ray, as you've seen, is very gullible despite how intelligent he is. He can put two and two together, but if there is any clue that seems to counter his line of thinking, he freezes. He's brilliant in other areas but he lags behind Charmy due to his naivety and his cowardly nature. A good detective has to take leaps of faith in his hypothesis and Ray just doesn't have the confidence for that. Until he does, he'll stay behind Charmy.
And Mighty is... well he's not a detective. XDDD He's not smart enough to be a detective, though that doesn't mean that he's an idiot. Mighty just has a normal level of intelligence, he's just surrounded by people that are smarter than him, or in Charmy's case, more experienced than him in detective work. Don't feel bad for him though, Mighty is leagues and bounds above most of the group in a lot of other areas: cooking, cleaning, fighting, moral boosting, storytelling, and a bunch of other stuff that you'll see in future chapters. If he gave it a try and tried to learn from Vector, I'm sure he would be able to get a basic understanding of detective work, but he's just not interested.
So hopefully that clears that up for anyone who was confused about the detective hierarchy of the Chaotix.