They'd have to be very similar to qualify as plagiarism. The fantasy genre is such a well-worn shoe that it's impossible to create something which bears no resemblance to someone else's work.
I'm not calling Rowling a plaigarist...BUT if you look at the collection of Tim Hunter stories (the ones started by Neil Gaiman and continued by others), you'll read the story of how a smallish, skinny, bespecticled brown-haired British pre-adolescent with a magic owl grew up to become one of the greatest mages humanity has ever seen.
As my old theology professor once said- "There seems to be a great deal of literary dependance here..."
Adding fuel to the fire is how closely the actor and wardrobe for the Potter movies resemble Tim Hunter, especially about the face. (For proof, do a little searching on the web. Amazon typically has both Potter & Hunter books for sale.)
However, Gaiman's Hunter has no Hogwarts...his lessons are more the "school of hard knocks" type, with occasional pointers from older supernatural types. Its grittier.
I liken it more to what happened when Superman died. Not only did Marvel dust off its various Superman-inspired characters (Hyperion, Gladiator, Thor) for higher profile duty, but all of the smaller independents making superhero comics introduced their own takes on the Superman legend. Dark Horse had one, Titan, go insane and start killing people. Image's Supreme was arrogant, aloof and alien- humanity was beneath him. And so forth.
Tim Hunter and Harry Potter have many similarities, yes. But they're taking fairly different paths, and not even headed towards the same destination. Potter's going to a hero's Heaven...but Hunter keeps flirting with Hell.
