This ones a close call because it's a battle of the bitches
Midhawk - Has run away from every single significant challenge in the entire manga so far. He has canonically bitched out from fighting Shanks THREE TIMES, he bitched out from fighting Crocodile, Vista, Marines and Luffy. Luffy in particular is interesting, Midhawk was raring to go fight Luffy when he was a rookie with no haki sailing along the east blue, but as soon as he turned into G5 Yonko Luffy, all of a sudden Midhawk starts sweating at the thought? I guess he doesn't want that fight anymore. That's the furthest thing away from a conqueror. His vivre card claims he's looking for a challenge but he lives in paradise with some monkeys and a ghost girl and doesn't dare go anywhere that would give him a challenge. That's like Steven Seagal claiming he's the best fighter in the world but hasn't won a single fight on record against anyone of note.
Fujitora on the other hand was reasonably solid but he backed down from Doflamingo even when Doflamingo threatened to straight up kill him. Fujitora rolled some dice to see if he should arrest Luffy... think about that for a second... a military leader deciding whether to arrest someone based on rolling dice. He gouged out his own eyes, because apparently he thinks shutting his eyes means evil doesn't exist like a 2 year old. He then developed some of the best observation haki in the series so he could see everything...
Overall I would say Fujitora is the conqueror because his poor decisions are more based on stupidity than being a bitch. At the very least he can claim to have challenged Greenbull/Akainu and was bold enough to make enemies of all the warlords in a single day.
Midhawk is just the Steven Seagal of one piece, his decisions are based on cowardice and he really can't claim to have done shit.