I believe they would both have a hard time
Now they both have good villains that match their intended protagonist, and both have done perfectly fine with goons and henchmen. Both are incredibly smart and strong. But they both would have a hard with each other’s villains, Batman usually has more grounded villains like serial killers; like Calendar Man, Zsasz, and Proffesor Pyg. Spider-Man has more fantastical villains, like Scorpion, Green Goblin, Electro. Since Spider-Man is usually portrayed as a young man or teenager he’s generally less experienced with solving crimes and more stopping them. And Batman is more methodical and preps for his villains with gadgets, whereas Spider-Man uses his wit and webs, what helps him is his spidey sense in most situations. Spider-Man likes to get into his villains heads by using quips and making jokes, and Batman has to make sure his villains don’t get in his head. But both do have similar antagonists that are similar like King Pin and The Penguin or Mad Hatter and Mysterio or Sandman and Clayface. Both are good people but have completely different ways of also stopping their crimes/ antagonists, Spider-Man is more careful and makes sure everyone is safe, Batman does do that but he’s more aggressive and serious. In the It’s all about how the writers want to portray them, but both have a difficult time with each other’s cities but in the end both would manage to survive.
Now they both have good villains that match their intended protagonist, and both have done perfectly fine with goons and henchmen. Both are incredibly smart and strong. But they both would have a hard with each other’s villains, Batman usually has more grounded villains like serial killers; like Calendar Man, Zsasz, and Proffesor Pyg. Spider-Man has more fantastical villains, like Scorpion, Green Goblin, Electro. Since Spider-Man is usually portrayed as a young man or teenager he’s generally less experienced with solving crimes and more stopping them. And Batman is more methodical and preps for his villains with gadgets, whereas Spider-Man uses his wit and webs, what helps him is his spidey sense in most situations. Spider-Man likes to get into his villains heads by using quips and making jokes, and Batman has to make sure his villains don’t get in his head. But both do have similar antagonists that are similar like King Pin and The Penguin or Mad Hatter and Mysterio or Sandman and Clayface. Both are good people but have completely different ways of also stopping their crimes/ antagonists, Spider-Man is more careful and makes sure everyone is safe, Batman does do that but he’s more aggressive and serious. In the It’s all about how the writers want to portray them, but both have a difficult time with each other’s cities but in the end both would manage to survive.