Marvel has plenty of powerful villains, but few who can hold a candle to Galactus, the Devourer of Worlds, and Dormammu, Lord of the Dark Dimension. Both entities have proved their vast amounts of power many times throughout the history of Marvel Comics. Dormammu is the sworn enemy of the Sorcerer Supreme, time and time again giving the strongest magic-users of the Marvel Universe a run for their money. Galactus is a being from before the dawn of reality, capable of consuming entire planets to feed his cosmic hunger. But while each villain is a threat any Marvel hero should fear, it turns out one is far more powerful than the other.
Dormammu is the god of his own realm and the keeper of the Dark Dimension, with a mission to spread his corrupt magic across the multiverse. The Sorcerer Supreme Doctor Strange has generally been successful in holding back the villain, but generally through trickery or smart use of his magic rather than sheer power. In Guardians of the Galaxy Vol. 1 #36, Doctor Strange reaches the level of the Ancient One and challenges Dormammu to a cosmic battle after the demon tries to take over the universe once again. Their battle rages across the cosmos and ends with Doctor Strange's utter defeat, proving Dormammu's superiority against the most powerful sorcerer in the universe at that point in time.
Galactus is older than the Marvel Universe itself, hailing from a prior version of reality. At the end of his own universe, he merged with the pure cosmic power of Metatron to become a necessary component of the very cycle of existence. The reputation of Galactus' power level proceeds him, but it's a power that must be constantly fed by devouring entire planets. Galactus is responsible for the deaths of billions of life forms across the universe, though their unwilling sacrifices are arguably worth it when one considers Galactus' larger deeds and purpose. Galactus will use his power to oversee the dawning of the next universe, and it has been revealed that he is the only thing stopping the spirit of destruction known as Abraxas from being released into the universe. Galactus is constantly battling back a godlike evil force with enough power to level all of existence, even when attending to other matters such as taking on groups of Celestials or helping to push back the Annihilation Wave.
In the fan favorite issue Doctor Strange #15 by Barry Kitson and Mark Waid with Scott Koblish and Brian Reber, Marvel answers the question of what happens when Galactus and Dormammu clash. In the issue, Galactus is banished to Dormammu’s Dark Dimension and consumes a planet that resides there. Since the order of that universe is ruled by chaos magic instead of science, the energy Galactus absorbs is different from his own universe, giving him magical abilities as well as his already present Power Cosmic. It turns out Dormammu orchestrated Galactus' power upgrade to use the Devourer of Worlds as a weapon to rule over all existence, but once Galactus learns of Dormammu's trickery, he consumes the demon, making it clear he's the bigger threat.
Both powerhouses draw power from their respective universes - hence why Dormammu is always trying to open a connection between Earth and the Dark Dimension - so logically this match-up would depend on where the battle takes place, but Marvel proved with the release of Doctor Strange #15 that even if Galactus was fighting the Dread Dormammu in the Dark Dimension, he is both stronger than the demon and able to adopt magical qualities in order to absorb energy in this alien reality. Galactus would easily defeat Dormammu outside the Dark Dimension, but it turns out that even on Dormammu's turf, he retains his power and has the means to grow even stronger. As is so often the case in the Marvel Universe, Galactus isn't so much a villain as a force of nature, handing him the win over Dormammu no matter where their battle takes place.