So I'm going to give my personal thoughts on this, and I think I might actually vote Jacket here with insane difficulty
Firstly, CH tracking down Jacket is honestly a 50/50 for me. Jacket was able to slaughter entire buildings of people (often with extremely loud guns) and escape without ever getting tracked down by the police and his murders going completely unsolved,
even in the level where police actively raided the building with him in it. CH is an excellent tracker, but Jacket is just weirdly good at getting away with his hits with no suspection from the police. Granted, Jacket has never shown any actual tracking abilities (he's given the addresses to almost every map in the game) so I think CH would probably find Jacket first before Jacket found them simply because of CH being a far better tracker than Jacket.
CH's only wincon here though would be to get the jump on Jacket, since I think in either a gunfight or a fist fight Jacket probably wins.
Firstly, Jacket is a monster in LS. Even using CH's higher-ends, Jacket could still ragdoll them. And Jacket is definetly one to use LS in his fights, so he'll probably be trying to rip CH apart. Another thing is that although CH is definetly more skilled, Jacket isn't bad either. He can kill a roomful of men with his bare hands pretty much instantly & is excellent at using melee weapons. He's also a veteran & has hand-to-hand training. The big problem here is that CH doesn't have prior knowledge. They know that this guy's former military & has a gun, but not that he's also a freak of nature in strength. This means that by the time CH realizes that this guy is superhumanly strong, Jacket will probably have ahold of them and will just rip their arms off and there would be nothing CH could really do. Countering this much of a LS difference isn't something CH can just skill their way out of. And keep in mind that Jacket can enhance their strength with masks, so they could just grow this difference even more if they wanted
In a gunfight, I'd agree that CH has better marksmanship. If you told CH & Jacket to hit a very specific spot on a target, CH would be able to hit it more accurately than Jacket. But in actual combat with a gun, Jacket definetly takes it. This guy has gunned down countless amounts of armed soldiers, mafia bosses, SWAT units, gangs, police officers, and has pretty much John Wicked entire buildings of highly skilled & trained people with immense combat experience no problem, not ever getting shot, stabbed, or punched once, and often using worse weaponry than his opponents in sub-par spaces, such as when he went against the police chief in the police station level. Afaik, no human IRL has shown this level of gunmanship where they could gun down entire squadrens of highly elite soldiers, cops, ect, entirely solo. It's just too much trained & intelligent people for a single person to realistically win against, but Jacket does it weekly with no issue. And that's not including the various masks that help Jacket in gunfights, such as:
All of this would only put CH at an even bigger disadvantage, so CH will be likely outskilled, outspeed, will likely loose Jacket in the middle of combat (seeing how good Jacket is at stealth like holy hell + the mask that makes him harder to spot), and there's the fact that Jacket could take a vital shot or 2 with his masks but a single good headshot from Jacket can kill CH, which makes me really doubt if CH can kill Jacket here
Really, unless CH can get the jump on Jacket (which honestly idk if that can happen given his enhanced senses + masks that improve his already great senses) then I don't really see CH winning this. Unless they both find each other while in the middle of driving & get into a car chase, which CH skillstomps in, but I highly doubt that's going to happen
So I'll be voting Jacket here