ABSTRACT: The argument of who would win in a fight, Harry Potter or Edward Cullen, has been argued since the later series came out. If we analyze the details of each fantasy world, however, I think we can find our answer quite easily, and this is my take on it.
Before I begin, I would like to say that I was an avid fan of Twilight for a chunk of time in my early teens, as well as Harry Potter, and I'm as familiar with each series as I am with the other.
If Harry Potter were to battle Edward Cullen, who would win?
Let's first take a look at the background and history of each character, as that will play a large role in the face-off. Edward Cullen was a normal seventeen-year-old boy when he fell fatally ill of the Spanish Influenza. His parents both died, and had he not been found by Dr. Carlisle Cullen, he would have died too. Carlisle was a vampire, and he bit Edward to save his life. Edward became an immortal vampire as well, with a whole new body. These vampires are immeasurably strong and fast. In the books, they have been described as able to snap a human neck with a twitch of the finger, or bite through flesh like butter. Some of them have supernatural powers. Edward happens to be the fastest vampire in the Cullen family, and he is capable of reading minds (or rather, "hear thoughts," as Snape has informed us (OotP pg. 530) that "Only Muggles talk of mind-reading. The mind is not a book, to be opened at will and examined at leisure.") After over a hundred years of his life as a vampire, Edward met Bella, a normal human girl, and they fell in love. Edward finds that he cannot hear Bella's thoughts, and in Breaking Dawn, they discover that this is because she has a natural shield in her mind, protecting it from penetration.
Harry was orphaned at a very young age, after Lord Voldemort, the most powerful Dark wizard of all time, murdered his parents. Voldemort also tried to murder Harry, but the magical protection given to him by his mother's sacrifice caused the curse to rebound, and Voldemort was temporarily destroyed. The feeble soul of Voldemort left the country to hide for thirteen years. During that time, Harry was raised by his horrible aunt and uncle. When he was eleven, he discovered he was a wizard with magical powers, and went off to Hogwarts School of Witchcraft and Wizardry. He made two best friends there, Ron and Hermione. Through their six completed years at school, they found themselves in many dangerous situations, gradually discovering complex and hidden magic and uncovering the mysteries of Harry's past and his connection with Lord Voldemort. When Voldemort returned to power, Harry was fourteen, and by the time he was seventeen, the world had become a very dangerous place. The trio did not return to Hogwarts for their final year of schooling, but went on a long (and slightly depressing) quest to destroy Voldemort once and for all. When Harry and Voldemort met in the forbidden forest at the Battle of Hogwarts, Voldemort tried to kill Harry, and Harry nearly died from the curse. He found out that he had a piece of Voldemort's soul latched to him, but when he had been attacked in the forest, that bit of soul was destroyed. He woke again, and returned to the school to face Voldemort for the final time. This time, he came out victorious. He fell in love with Ron's sister Ginny, who is also a fiery and accomplished witch, and Ron and Hermione fall in love as well.
We now have to decide at what stage in Harry and Edward's life we are holding this figurative face-off. I am inclined to say that it occurs after Harry's victory over Voldemort, while he is seventeen years old, the same age as Edward. However, to make it fair, we shall say that this is after Edward's series has ended, too, when Bella has become a vampire and Edward has a daughter.
Let's say they are both standing, facing each other in a large open space. It is easy to say that Edward can hear all of Harry's thoughts, and thus is able to predict his move before he makes it. However, we already know that a mental shield against Edward's ability is possible; Bella has it. Harry is capable of Occlumency now, so he has his own shield against it. It is true that his Occlumency abilities were dismal when Snape first began teaching it to him, but there was a moment in the Deathly Hallows, while Harry is digging Dobby's grave, when he has a sort of epiphany and is able to close his mind properly. So we can safely say that Edward has lost that advantage.
Edward is impossibly fast. This will make it highly difficult for Harry to cast spells at him and hit his target for sure. We know that it is possible for wizards to dodge some spells if they can react quickly enough, and Edward is clearly capable of doing this. He is also incredibly strong, and his skin is nearly impenetrable. Harry will have a very difficult time cursing Edward directly, and we do not even know the rules of magic on a vampire's skin; Hagrid, being half-giant, was protected against most spells. Would Edward be protected like this, too? If not, the Impedimenta jinx would work against Edward to slow him down considerably, if Harry could hit him. If not, Edward has all his natural speed.
But Harry also has the Shield Charm on his side. We saw in Deathly Hallows that the shield blocks both physical attacks as well as most spells. If Harry uses this charm, he can prevent Edward from ever touching him, which is really Edward's only weapon. However, the battle is who would win, not who would defend themselves best, so Edward might still have a chance.
If we assume that one spell alone cannot make an effect on Edward, and that Edward is unable to touch Harry with his shield, then we may have to bring in the assistance of each young man's friends, or our heroes will be trapped in limbo forever. Edward's posse includes all of his vampire family: Alice, Jasper, Emmett, Rosalie, Esme, Carlisle, and Bella. Perhaps he can rope his "werewolf" (though technically they are shape-shifters) pack into helping, too. One can argue that Edward's family has connections to all the vampire families that came to help in Breaking Dawn, but there's also the point that Harry is a global hero in the wizarding world, and if he asked for it, hundreds and hundreds of wizards would come to his aid. If this were the case, Harry's victory would be unavoidable; we know that perhaps a vampire is immune to a single spell, but we've seen that when a group of wizards casts the same spell at the same time to the same opponent, that the spell is immeasurably more powerful and effective. If hundreds of wizards battle a few dozen vampires and shape-shifters, the wizards will come out better off.
But, to avoid all that chaos, let's keep it at the closest friends and family; those each character interacts with most regularly. So: Edward has 7 other vampire family members, plus the seventeen werewolves/shape shifters that were present in Breaking Dawn, and we'll even throw in the Denali vampire clan (Tanya, Kate, Eleazar, and Carmen) So Edward has twenty-eight allies at this point.
Harry has the whole of Dumbledore's Army following him. That's twenty-eight students, not including Fred *sob* (most of whom are fully qualified by the end of the seventh book): Hannah Abbott, Lavender Brown, Katie Bell, Susan Bones, Terry Boot, Cho Chang, Michael Corner, Dennis and Colin Creevey, Mariette Edgecombe... you get the idea. Then we have the whole Weasley family: Molly, Arthur, Bill, Charlie, and Percy. (All the other children are included in the DA count). Then there's the other ten remaining members of the Order of the Phoenix. At a total of 43 allies for Harry, we don't even have to throw in Kreacher, though his elf powers might be of assistance.
So with Harry's side nearly doubling Edward's side, Harry's far better off. However, there are some helpful vampires with supernatural powers going for Edward: Kate can cause hideous pain through her touch, Eleazar senses other powers in vampires (not much help in battle), and Alice can see the future (maybe she should tutor Professor Trelawney!). Kate can be repelled with a Shield Charm, but Alice's power can't be contended. She'll be able to predict what move her opponent will make before they make it, though she has no ability to block a spell.
Sidenote: A spell that might have a chance against Alice could be Incarcerous, a spell that binds the victim in ropes. From what we've seen, we can deduce that someone cannot simply dodge a beam of light to avoid the curse; the ropes will find them. Alice may have supernatural strength, but these are magic ropes we're talking about.
Then there's the whole concept of the werewolf/shape shifters. They may be huge and powerful, but they don't have extra-hard skin that blocks physical attack, so they will be susceptible to anything cast from a wand. They also have weird, inter-connected minds, which leaves me to wonder: if a wizards casts the Imperius curse on any one werewolf, will it then control all of them? This would be a sure and easy advantage for Harry. Imperio may be an Unforgivable Curse, but we've seen in DH that Harry is willing to use this spell in mortally dangerous situations, and having twenty-eight supernatural creatures charging you would probably fall into that category! Even if the curse only controls one wolf at a time, multiple curses will have the whole wolf pack under wizards' rule. Plus simple Stunning spells would greatly reduce their numbers.
I simply can't get past the simple fact that vampires and werewolves can't cast spells or block magic, and wizards can. Forty-three able wizards (make that forty-two; Arabella Figg, a Squib, was counted in the Order numbers) with hundreds of spells, curses, hexes, and jinxes at their liberty against twenty-eight mythical creatures with limited (but no less powerful) abilities? I think it's safe to say our wizards will come out victorious.
Harry looked up, diverted. The circumstance of Ron having read a book that Hermione had not was unprecedented.
JK Rowling Deathly Hallows
Quidditch started in the 11th century at a place called Queerditch Marsh, which is not marked on muggle maps because wizards have made the place unplottable. Originally it was quite a crude game played on broomsticks with just the quaffle.