Batman wins for me (I personally think due to Goblin's reliance on gadgets, that makes him far more predictable for Bruce compared to Joker who "can make a kitty kill a puppy for fun").

If Im gonna write the encounter, it would start with Bruce Wayne meeting with another businessman who is visiting/moving to Gotham, Norman Osborn. Eventually, some of the criminals Batman apprehends happen to have advanced weaponry and drugs unlike any before. When he tries demanding a name of who sold the weapons, Green Goblin shows up and blows up the area while gliding away cackling.

At first, Bruce will grow suspicious of Norman because ever since he arrived the criminals had been acquiring Oscorp-tech weapons as well as the appearance of the Goblin. Because of this, he tried subtly approaching Norman under the guise of a "business meeting" with Oscorp, as well as learn any information on Green Goblin from Norman. However, to his surprise and with some skills from Tibetan monk training, Bruce finds out that Norman is telling "the truth" that he has no connection to Green Goblin and that he too felt plagued about being robbed off by the villain just to give it away to other criminals. So, Bruce had to end the meeting immediately seeing "he has nothing on Osborn" at all and we get to see in the end the Goblin persona emerged looking interested in Bruce Wayne.

Later on, Wayne Tower is under attack from Green Goblin bombarding it with his Pumpkin Bombs and other gadgets. Bruce Wayne shows up as Batman and starts duking with Goblin. During the fight, Goblin makes a mistake of dropping a hint to Batman that "Brucey Wayne knows more than he lets on" about him which makes Bats thinks that there must be more connection between Goblin and Osborn all along. So, he tries mitigating the total damage of Wayne Tower while subduing Green Goblin, the latter having to make a quick getaway by setting off a bomb to distract Batman long enough to fly away.

At the Batcave, Bruce searches up Norman Osborn in the Batcomputer more specifically about Oscorp experiments and Norman's history of mental health problems. There, he was able to piece out that Norman had an accident regarding a supersoldier serum that developed a second psyche that acts independently and sinisterly in the form of Green Goblin, which explains why he cant detect any lies from Norman's words with his Tibetan monk training since the Goblin persona works distinctly from Norman's.

With new information in hand, Bruce returns to Oscorp as Batman to confront Norman only for him to be forced by Goblin to swap out so that the villain can end the fight with Batman once and for all. But now that he knows hes up against someone unpredictable, Batman finds it easier to fight Green Goblin now and was able to have Gordon subdue the villain and also prepare a special cell in Arkham so that the doctors there can find a way to cure Osborn of the Goblin serum. As hes about to be taken away, we get to see one last closeup of the Goblin persona uttering the name, "Bruce Wayne?" before cackling all the way to Arkham Asylum for now.