Yes and no. In a straight fight with no Prep Time, Bat's gets completely besmirched by Spidey. Everything Batman can do physically, Spiderman can do better. Batman can Bench 1,000lbs. Spider Man can Military Press 25
Tons. His speed, stamina, agility, balance and reaction time are all Superhuman. Add to this his Spider Sense and Batman can't lay a glove on him.
The Kingpin gave Batman a very tough fight. Spider Man with That Look in his eyes beat Fisk to his knees - then hauled him to his feet by his Man Boobs.
Prep Time changes things considerably. While Parker is a genius and has out-smarted more powerful enemies, Batman is past master of strategy. Given enough Prep Time, it's more than likely Batman could figure out a way to negate Spider Man's vastly superior physical abilities.