The history books and Rita Skeeter's trashy biography all say it was a legendary duel, but I'm convinced the actual outcome is more ambiguous. Dumbledore's own testimony suggests he 'defeated' Grindelwald in 1945, and that's the word the wizarding world latched onto. Yet, given their history and Dumbledore's profound reluctance to face him, I can't picture him delivering a killing curse. JKR's later writings hint Grindelwald was imprisoned in Nurmengard, which he built, and that feels more like Dumbledore's style—a permanent, living defeat rather than an execution. The man spent a lifetime avoiding direct, mortal choices with those he loved; finishing off Grindelwald in cold blood seems entirely out of character.
Ultimately, I think the duel ended with Grindelwald's magical defeat and disarming, not his death. Dumbledore likely placed him in that tower, a monument to his own fallen ideals, which is a far more complex and tragic victory. It fits the thematic weight of their story—a personal failure resolved with immense sorrow, not a clean, heroic kill. The 'who killed him?' question probably stems from later gossip and the fact that, to the public, a dark wizard's sudden disappearance after a fight can easily be morphed into a murder tale.