Spider-Man
Peter Parker's intellect consistently ranks among the highest in the Marvel Universe. He invented his web-shooters as a teenager using household materials, developed the sophisticated web-fluid formula, and has contributed to scientific advances alongside Reed Richards and Tony Stark. His understanding of physics, chemistry, and engineering operates at doctoral levels despite his youth.
His tactical intelligence manifests through creative problem-solving during combat. Spider-Man routinely defeats opponents with superior raw power through exploitation of environmental factors, psychological insight, and improvised technical solutions. He has outsmarted beings from Mysterio's illusions to Doctor Octopus's machinations. His quipping during combat serves dual purposes: psychological warfare against opponents and self-regulation of his own fear responses.
The Joker
The Joker's intelligence operates in a fundamentally different paradigm. His criminal genius manifests through elaborate schemes accounting for multiple contingency responses, understanding of human psychology at an intuitive level, and chemical expertise enabling creation of his signature Joker Venom compound.
His strategic brilliance derives partially from its apparent irrationality. Plans that seem nonsensical reveal devastating logic upon execution. He has orchestrated scenarios where every possible response by opponents furthered his actual objectives, including scenarios where his own apparent defeat constituted victory. The Joker understands psychological manipulation at savant-level proficiency, identifying emotional vulnerabilities and exploiting them with surgical precision. His transformation of Harvey Dent demonstrates intelligence as weapon more devastating than any conventional armament.