Freddy vs. Jason (2003) was the cinematic answer to many horror fans' question of: "If Freddy and Jason got into a fight, who would win?"
Director Ronny Yu delivered by bringing Robert Englund in as Freddy and nabbed stuntman Ken Kirzinger for the role of Jason, despite Kane Hodder's desire to play the role opposite his friend (Englund). The plot was riddled with holes and shaky at best, but the movie was never intended to be a masterpiece: it was meant to be a crossover between two of the most beloved slasher franchises and bring Jason and Freddy together to, presumably, see who would kill the other in a fight to the death.
The plot of the film revolves Freddy using Jason as a pawn to incite fear in the young people of Springwood again after they've forgotten about him. Jason, however, wants to rack up his own body count and does so without considering Freddy, which makes the dream demon quite upset. The ending, after the two finally started fighting each other, led to Jason rising from Crystal Lake with Freddy's severed head that winked in the film's final frame, implying that they had both, essentially, survived. So who would actually win?
Jason Voorhees: Powers and Abilities
Jason's origins have a lot of speculation about what he is, so that's important to consider when taking a look at his abilities. Once, he was human, a little boy with severe facial deformities and mental disabilities, who supposedly drowned in a lake. He didn't drown, but he did eventually get killed by Tommy Jarvis in Friday the 13th: The Final Chapter. Ironically, he was also resurrected by Jarvis in Friday the 13th VI: Jason Lives. Determined to ensure Jason was dead once and for all, Jarvis took a trip to his grave and stabbed him with an iron fence post; it started storming and a bolt of lightning turned that fence post into a lightning rod, sending volts of electricity through Jason's corpse and resurrecting him like Frankenstein's monster.
After that, zombie Jason was essentially invincible and his resurrection gave him super strength and stamina - he punched off a man head's in one blow (Jason Takes Manhattan). If considering his already formidable stature, high pain tolerance, weapon skills, ingenuity, and resourcefulness, he's certainly more than a fair match. Jason is single-minded and near unstoppable. People have tried to kill Jason in a multitude of ways, and even as a human, he was able to survive things like being hung, stabbed in multiple ways, and taking an axe to the skull.
Also, he's relatively invulnerable to complete bodily destruction since his demonic heart can hypnotize people, leaving them vulnerable enough for him to possess them and be reborn. If his heart was targeted in some way and destroyed, that would likely be a real end of him. Also, if he was incapacitated in a way that he couldn't regenerate (being cryogenically frozen, for example, as seen in Jason X), that would mean sure defeat if killing him outright wasn't an option.
Related: Freddy Krueger Was Almost In Friday the 13th Part 7
Freddy Krueger: Powers and Abilities
Freddy Krueger's stat card isn't as extensive, range-wise, but his powers are more than impressive. Though Freddy has been killed - he was burned alive by the angered parents of all the Springwood children he murdered - he isn't considered to be undead. Instead, Freddy is a dream demon who lives in the dream world where he is nigh invincible. His imagination and passion for unique kills is showcased in the alternate reality, plus he can shape-shift into numerous different objects or whatever he chooses in order to be menacing.
Where Jason is brawn, Freddy is most certainly brains and his unlimited imagination and brilliant, psychopathic mind may very well be an edge he needs in the fight. He isn't hardy or sturdy in build, but he has a speed and dexterity on his side, as well as an advantage whenever he's inside the dream world as he can influence anything in their surroundings, including his victims. Freddy feeds on fear, and, in doing so, can weaponize someone's fear.
He is certainly immortal, though it has been proven time and again that he's very vulnerable outside of the dream state. This has been exploited by potential victims who maintain control inside their dreams, gaining the ability to pull Freddy out of the dream state. Usually, they have to be woken up by someone on the outside physically waking them up, but someone could do it on their own as well.
And The Winner Is...
The winner is Jason Voorhees. Since Freddy would have to specifically target his heart or completely incapacitate him in order to be victorious, Jason has way more outcomes where he would be victorious overall. Although Freddy could suck Jason into the dream state, like he did in Freddy vs. Jason, there's nothing that says Jason couldn't become self-aware, like others have, and pull Freddy out of the dream world, leaving him entirely vulnerable to harm. Freddy could use his speed to deliver a fatal blow to the heart, but Jason's overall fighting skill is stronger, which means in hand-to-hand, he'd easily gain the advantage.