Well, this depends on how you want to argue this one. It's sort of like a Batman Vs. Superman argument. Harry Potter is a character who would arguably be based around planning and preparation. Like Batman if it's just a straight fight against Superman he's paste, but if he has a chance to prepare it's a lot more interesting. Consider for example that Superman's arch enemy, a guy who has defeated him before, is Lex Luthor, who is also 100% planning and preparation.
To make this point for example Harry Potter has the deathly hallows at the peak of his powers. He is by definition carrying a wand that makes him invincible, a cloak that makes him so invisible that not even death itself can find him, and a stone that lets him come back from the dead. Even at the end of the series he still has the cloak.
While not used to it's full potential in the series it should be also noted that Hogwarts has access to temporal manipulation devices like the "Time Tuner" which Hermione had, which as used in the stories can be used to allow Harry a second chance at anything (needless to say this wasn't used more often).
To put this into perspective if one argues not even the metaphysical force of death can detect Harry when he's invisible, it would work on Vegeta, this would guarantee Harry the first shot if he approached that way and he could easily turn Vegeta into something harmless like a mouse and then feed him cheese for the rest of his existence. Even if one argues Vegeta got the first shot it can be argued he would indeed kill Harry, but if he had possession of the right artifacts, especially using them in conjunction, he could come back, and then do the same basic thing. See one can argue that Vegeta can return from death as well (death doesn't stick from what I've seen in DBZ) but Harry has the ability to prevent that by just rendering Vegeta powerless.
It goes beyond the scope of the series to know what would happen if say Harry prepared for the fight by say using a strand of hair from another DBZ being more powerful than Vegeta and then assumed that form as well, something capable of withstanding an initial attack inherently even if Harry didn't have the practiced fighting skills, of course with enough Polyjuice potion and patience one could make a case for him turning into a magic using super-saiyan or whatever as long as he kept dosing.
I didn't answer the poll because my answer is a "it depends on the circumstances", and I confess I tend to take the underdog side in cases like this. In short if stealth and guile are allowed to enter the equasion then yeah, Harry would take him down easily. To be honest I don't even think Harry is less powerful as he develops, he can do more with his power than Vegeta can do with his (it's all geared towards destruction) it's mostly a question because Vegeta is so bloody fast, and both characters could end it with one strike. Of course it should be also noted Harry Potter as a mature wizard can teleport like a lot of DBZ characters can, he's just prohibited from doing so for most of the books so it rarely comes up, and teleportation gives him one of the quintessential ways of avoiding a DBZ level attack. That said I do think his cloak of invisibility is going to be the real clincher here because it's not a *normal* cloak of invisibility which also exist in that world apparent, it's powerful on a metaphysical level. Another argument I'd also raise is we do not know what the upper level of wizardly defenses are, mostly they block each others spells, we do not see them really facing an overwhelming physical or energy based attack, one could potentially argue that if he was ready Harry, like most wizards, could deflect a destructive attack like one of Vegeta's with a simple gesture of his wand, especially if Vegeta used energy, but still I think the point made about teleportation is Harry's best defense.
I'm sure many people will overlook my points though (hey I think they are some good ones). After all it seems the majority are deeply committed to Harry as the loser.... come on Potter fans, join me and rally!
To make this point for example Harry Potter has the deathly hallows at the peak of his powers. He is by definition carrying a wand that makes him invincible, a cloak that makes him so invisible that not even death itself can find him, and a stone that lets him come back from the dead. Even at the end of the series he still has the cloak.
While not used to it's full potential in the series it should be also noted that Hogwarts has access to temporal manipulation devices like the "Time Tuner" which Hermione had, which as used in the stories can be used to allow Harry a second chance at anything (needless to say this wasn't used more often).
To put this into perspective if one argues not even the metaphysical force of death can detect Harry when he's invisible, it would work on Vegeta, this would guarantee Harry the first shot if he approached that way and he could easily turn Vegeta into something harmless like a mouse and then feed him cheese for the rest of his existence. Even if one argues Vegeta got the first shot it can be argued he would indeed kill Harry, but if he had possession of the right artifacts, especially using them in conjunction, he could come back, and then do the same basic thing. See one can argue that Vegeta can return from death as well (death doesn't stick from what I've seen in DBZ) but Harry has the ability to prevent that by just rendering Vegeta powerless.
It goes beyond the scope of the series to know what would happen if say Harry prepared for the fight by say using a strand of hair from another DBZ being more powerful than Vegeta and then assumed that form as well, something capable of withstanding an initial attack inherently even if Harry didn't have the practiced fighting skills, of course with enough Polyjuice potion and patience one could make a case for him turning into a magic using super-saiyan or whatever as long as he kept dosing.
I didn't answer the poll because my answer is a "it depends on the circumstances", and I confess I tend to take the underdog side in cases like this. In short if stealth and guile are allowed to enter the equasion then yeah, Harry would take him down easily. To be honest I don't even think Harry is less powerful as he develops, he can do more with his power than Vegeta can do with his (it's all geared towards destruction) it's mostly a question because Vegeta is so bloody fast, and both characters could end it with one strike. Of course it should be also noted Harry Potter as a mature wizard can teleport like a lot of DBZ characters can, he's just prohibited from doing so for most of the books so it rarely comes up, and teleportation gives him one of the quintessential ways of avoiding a DBZ level attack. That said I do think his cloak of invisibility is going to be the real clincher here because it's not a *normal* cloak of invisibility which also exist in that world apparent, it's powerful on a metaphysical level. Another argument I'd also raise is we do not know what the upper level of wizardly defenses are, mostly they block each others spells, we do not see them really facing an overwhelming physical or energy based attack, one could potentially argue that if he was ready Harry, like most wizards, could deflect a destructive attack like one of Vegeta's with a simple gesture of his wand, especially if Vegeta used energy, but still I think the point made about teleportation is Harry's best defense.
I'm sure many people will overlook my points though (hey I think they are some good ones). After all it seems the majority are deeply committed to Harry as the loser.... come on Potter fans, join me and rally!