My Hero Academia and Fullmetal Alchemist: Brotherhood feature two very different systems of magic. The former has superhero/villain Quirks, while the latter has alchemy. In a battle between MHA's Stain the Hero Killer and FMA's Edward Elric, who would be victorious?
Stain's Powers & Skills
Stain is primarily a melee hero, even though his Quirk (Bloodcurdle) doesn't actually augment his physical abilities at all. He's trained himself in the ways of the assassin, to the point that he can move and strike without warning and take even battle-hardened pro heroes by surprise. In the anime, Stain can move with astonishing speed, flashing through the air to evade heroes' attacks and maneuver into a position to strike back. Even Izuku Midoriya, with his well-honed use of One For All, struggled to keep pace with Stain's movements. Stain has formidable agility and technique, with the physical strength to match. Most of all, Stain has the mind of an assassin, knowing how to stalk a pro hero and follow them without being detected. Then, Stain can find the perfect opportunity to strike and ambush heroes when they're alone and vulnerable.
In combat, Stain has a jagged katana that can not only be used as a regular sword but also as a blood sample collector. The same is true of the many knives that Stain keeps on hand. Stain collects blood to fuel his Bloodcurdle Quirk, which will paralyze the blood's owner once Stain ingests that blood sample. The exact duration of the paralysis depends on the blood type, but in most cases, it hardly makes a difference. Stain will quickly finish off his target long before his Quirk's effect wears off. He very nearly killed Tensei Iida this way.
Edward Elric's Powers & Skills
Edward Elric once committed the grave sin of attempting human transmutation along with his brother Alphonse. As a result, Edward lost his right arm and left leg, replacing them with tough, high-grade automail versions that not only restore his mobility but give him the element of surprise against his foes. Edward can block an enemy's blade with his bare arm, a clash of metal on metal rather than metal cutting into muscle and bone. What is more, Edward can perform alchemy without transmutation circles at all, having seen the Truth, so he only needs to clap his hand together to perform alchemy.
In a fight, Edward can use his advanced martial arts technique and short stature to evade his enemy's attacks, and he is graceful and agile in combat. Edward strikes with regular kicks and punches (he loves kicking), and he can reshape his right arm into a blade to slash or stab his enemy. Edward can pair his martial arts with alchemy, creating barriers, conjuring pillars that quickly strike the opponent or breaking down objects to create resourceful attacks. He once broke down soggy dynamite sticks, for example, to release ammonia gas and overwhelm his two opponents' strong noses. Edward is also adept at setting up hunting snares, such as that time he caught the ninja-like Lan Fan and suspended her in the air by the ankle.
Stain Vs. Edward Elric - Who Wins?
This fight is one that will be fought at close range, though Edward does have some ranged options that Stain lacks. Stain will begin the fight on his own terms, ambushing Edward from the shadows in an urban battlefield to try and draw blood. Ed will surprise him with his quick moves and metal arm, evading Stain's blades and blocking them with his automail right arm. Stain will keep trying to engage Ed at close range, only to be stymied by Ed's automail arm and agility. Edward can now return fire with his alchemy, but Stain is even more maneuverable than Ed is, and Stain can quickly evade any of Ed's alchemy-based attempts to strike or capture him.
Stain will retreat to the shadows, and he will realize that Ed's right arm is impervious to his attacks and thus, his Quirk. So, it's time to get crafty. Stain will strike again and take Ed by surprise, this time by attacking Ed's left side, to check if Ed's left arm is also impervious. Stain may entice Ed to make wild alchemy attacks and kick up a lot of debris and dust, and this will work to Stain's advantage, who just needs to land one surprise blow. Once Stain finds a chance, he'll finally land a glancing blow on Ed's arm or cheek, and collect his blood sample at last. Once Ed is paralyzed, he can't use alchemy at all, and Stain can finish him.