Not really. He is more powerful than Roy but he is not all powerful.
Will all his powers? He's about as close to all powerful as it gets. As I said, if PS gets everything he can do, Roy should get a false philosophers stone. It's only fair.
Fine. Since we never even see what he could do with a Philosopher's stone, he'd probably be a step above Kimbley, who was already kind of all-powerful, so it'd be about a fair fight then.
Let me give an idea of how I think that would go down.
Problem Sleuth lands on one side of the battlefield, scythe in hand and vampire powers at the ready. He charges forward, only for a tidal wave of flame to come at him. He swings the scythe, stopping the flames, only for another flame to slice across his hands, forcing him to drop his scythe. He runs, more fire peppering him as he runs before hopping inside a building for protection. He leans out and tries some DIPLOMACY, only for Mustang to dodge the volley. As he tries again, Mustang simply burns the gun to a crisp, detonating the bullets and hurting Problem Sleuth enough to make him run. He leaps out the building just before Mustang detonates it, turning it into rubble and sending our noir-ish hero rolling right back up to the scythe.
He takes it and leaps at Mustang, taking a swing as Mustang sends a small bolt of fire. The scythe cuts into Mustang's abdomen, but as a result Problem Sleuth is blinded, his eyes burned to cinders. As he swings wildly around, Mustang cauterizes the wound, sending him to his knees as a lucky blow from the scythe lands on him, getting stuck as Mustang grabs a hold of it, ripping it out of the detective's grip. He snaps his fingers as a wave of fire incinerates the poor detective.
Mustang rips out the scythe and limps off the battlefield, nearly broken but still alive. In the afterlife, Problem Sleuth escapes as he always does, though by the time he's out the battle has been declared a victory for the Colonel.