Is any of them smarter than Red John and James Moriarty?
And who would be the champion who will solve the case as fast as possible?
My opinions about Moriarty:
Hercule Poirot vs. James Moriarty: I don't think Poirot can handle a criminal mastermind. I think Poirot is more of an expert in regular criminals, or regular people who commit one-time crimes for personal gain. Poirot has made mistakes oh but lots of times... if you have read the story The Chocolate Box, or The Lost Mine. Indeed in "The Mysterious Affair at Styles" it takes him the better part of 3 months to solve the case.
Mycroft Holmes vs. James Moriarty : I think Mycroft is as smart and possibly even smarter than Moriarty, but he is not motivated. He collects and collates information, as opposed to investigating or countering someone else's moves. In a duel of some sort with Moriarty, if he weren't ready at the outset, he'd spend the rest of his time playing catch-up.
Miss Marple vs. James Moriarty : This would be fun to see, as long as violence did not somehow enter the picture. I can picture her meeting Moriarty in some situation where he was on his best behavior and she being the only person at the dinner table to be immediately aware that he was up to something, kind of like Sandra Bullock's immediately being on to Ryan Gosling in Murder By Numbers.
Liutenant Columbo vs. James Moriarty : Columbo has the advantage of the 6th sense that tells him exactly who the guilty party is at the outset. His mode of operandi is to find the one piece of their alibi that doesn't fit and then pester them endlessly until he figures out what that one missing piece reveals or until they crack under the pressure. Moriarty would be tough for him because he wouldn't leave any clues or out of place bits of evidence, and even if he did, he would disappear as soon as he realized Columbo was onto him. Most of Columbo's cases were about people who only committed the one crime because they felt they had to. A career criminal like Moriarty would probably make his murders look like accidents and Columbo would never even be called to the scene.
Nero Wolfe vs. Moriarty : I think of Nero as a more proactive Mycroft, focused more on deduction than collection/collation and he has Archie Goodwin doing his legwork for him. The problem is that Nero works for hire to support himself, so if a case was brought to him involving some crime of Moriarty's, Moriarty would already have had the head start. It would be up to Archie to fight his way across Moriarty's local crew until he got information, pointing to Moriarty, and by then Moriarty could be in the wind.... except that he wouldn't. He would take the opportunity to break into Wolfe's townhouse and confront him directly. This would lead to Wolfe having to get up and fight, or to have to shoot Moriarty if he had a pistol at hand. Let's hope Archie gets back in time.
Moriarty vs. Horatio Caine : There is something in the Miami air that 1) turns it orange and 2) lowers people's IQ's and makes them take crazy risks and bluffs. Moriarty might fly into Miami as the cold, calculating methodical conductor of crime we all know him to be, but after a few hours of the swishy camera work and techno drums, he would be as reckless as a tweaker trying to beat a red light. In no time at all he would be trading quips with Horatio Caine and be wondering why they weren't snappier, as Caine gave him one whispery non-sequitur retort after another. In the end, Moriarty is going to end up standing in front of his car, dropping his weapon, and putting his hands up before Callie Duquesne puts a round in him.
Do you ever read Kim Newman? He's done some superb Moriarty stories, like this one! http://www.bbc.co.uk/cult/sherlock/shamblesinbelgravia1.shtml
Mycroft Holmes vs. Sherlock Holmes-what if Mycroft Holmes becomes the greatest mastermind ever and Sherlock need to figure it outthat Mycroft really is a criminal, and needs to be stopped could Sherlock stop Mycroft? Mycroft Holmes, his box of toys includes espionage, so there certainly is some overlay with his brothers world of crime. According to Sherlock Holmes himself, Mycroft is smarter than him and possesses the same observational and analytical skills, but given his physical condition (being obese), he is far too lazy to run around as detective like Sherlock does. How much he understands of actual criminology is open to debate, but given his genius and his position in her Majesties Secret Service, I would be more scared of getting on Mycrofts bad side, than Sherlocks. Even a Moriaty would think twice of messing with that guy, assuming, he knew of his existence.
It would be different if Mycroft was just an algebra teacher (ironically Moriarty's cover), a doctor or philosopher. Mycroft's big backdraw is primary his laziness. He is a general, not a foot-soldier, who gets his hands dirty, like his brother usually does.