Okay, so I'll start out by saying that Cole takes this.... barely. Like, 6/10 decision right here and John is gonna give him hell hefore this fight is over.
So, let's start with what John can do.
Firstly, his summons. Nannasprite is the same tier as him, can fly, provide John healing items, go through walls at will, create platforms for John to stand on and ovens that can launch projectiles (or John himself if he decides to hop in). Her most dangerous ability, however is her Fusionism. If she comes into contact with any physical object for too long, she'll fuse with it. People included. She gets her habds on Cole for too long, John'll have a handy dandy new ColeNannasprite at his desposal. Luckily for Cole, this isn't in character for either of them.
John can also fly with his jetpack or launch himself via his Spring Hammer (forget the name).
In terms of skill, John completely blows Cole out of the water. John is one of few in his Session to go God Tier, impressed Vriska to the point where she considered him on her level (keep in mind Vriska is a massive narcissist who has been killing people sense she was born, has repeatedly stomped Eridan, who himself has studied every notable battle in Alternian History and has High 4-C weapons at his disposal, and was the only one in her session who went God-Tier. She's one of the most skilled characters in the comic, short of any of the Striders.) He's done all of this without any form of formal training. SBURB was a game that was literally designed to turn people into gids and usually killed most of them by the end. John kept his team alive to the end of his session despite being the only one on his team without some kind of training or skills developed beforehand and does so agai right afterwards, albiet at that point he's 2-A.
Close quarters is self explanatory. Skill, AP, and hit based time stop murk Cole there.
John could also Captchalogue the RFI off his back if gets close, which he'd likely attempt one he sees Cole's clearly drawing power from it.
The absolute biggest card in his deck is his Weather Manipulation. He can create tornados that cover entire islands. He can easily launch Cole to the other end of the Earth with that thing. But only when out under extreme pressure. He has no control of it and actually sent himself flying the first time he used it. Him and everyone else on the planet in fact. If Cole's too zealous in his offensive, it's over.
TL;DR, if John gets in close, Cole is dead. And thanks to the above options, he stands a good chance of doing that.
Cole still wins however. His stat amps can help brudge the gap, he can blast John back once he gets close, can destroy his jetpack with one good hit, has experience with multiple opponents, and has way more versatility.
His Regenerationn trumps John's healing, soley do to not being inventory based and incap methods prevent the "backfiring offensive" mentioned earlier. Nannasprite could free him, but Cole can easily dispatch her. She doesn't spam intangibility and her range is comparatively terrible. Homing missile spam deals with her.
That said, incap is really his only reliable way of winning this. Everything else runs the risk of taxing John enough to sommon a storm, which could potentially one-shot, if not severely cripple him. Not to mention John's own endurance (this guy tanked being eaten alive at one point).
But Cole can definitely hold out long enough to establish control if the fight, flying just out of John's grasp, keeping him and his sprite in check via superior environmental awareness and control. Worst case scenario, resurrection, provided John's blows don't crush his skull.
If Cole flubs up once, he dies. If John gets a hit in the RFI, Cole dies, as John can just charge through his attacks at that point. If Cole presses John to much (not out of character for Cole and his abilities can easily press him to much. Karmic Overload and Ionic Storm combo come to mind) he dies.
Cole walks away limping, but he walks away victorious.