I'm in a debate about who is more intelligent, Superman or Batman. One part we are stuck on is whether mental stability should hold influence. As far as I know, Batman's will is unbreakable. Despite any tragedy, he stands by his code and despite any hardship he remains level-headed and thinks his way out of anything. Superman has been shown to be breakable. Red Sun and Injustice show a Superman very vulnerable to corruption and suggestion, as well as a strong arrogance and narcissism that leaves him vulnerable to attacks. If alternate universes are not your thing, then Villain's Journey shows Batman, and even Hal Jordan, resisting Graves' mental attacks, while Superman is in literal tear taking it the worst of the group. Superman is cocky, egotistical and corruptible. So, is that a mark against his intelligence or simply his character?
Beyond that there is the simple version of who is more intelligent. 12th level intellects can process 12 genius thoughts simultaneously. Superman simply thinks fast and acts faster. The inner workings of his mind are impossible to tell. However, much of what he does is banking on his invulnerability to give him another shot if it doesn't work. Any plan that pops into his head he can enact with super speed and try again when he's done. Batman gets one mistake and its over, so he weighs everything at an incredible rate. As the league's tactician, Batman can quickly assess situations and maximize potentials, but the inner workings of his mind is impossible to know. So is Batman's position a sign of Superman's deference to Batman's intelligence? By DC standards, who do you think wins out?