A lot of people in the forums i have read say Harry is not in the class of the Voldermort, dumbledore and Grindelwald and they point to elements in the series in which Harry's continued triumph is more luck than skill. On the other hand others claim Harry is in that class and point to instances in the series when Harry did something spectacular or when someone mentions the fact that harry is powerful e.g. the fact that Hermione tells Harry that only a very Powerful wizard can produce a patronous powerful enough to repel all those dementors and she said this before even Harry himself knew that He had conjured the Patronous. I agree with the latter i think harry was powerful how ever my reasons are more from a logical point of view than the actual written events and allow me to show you my reasoning.
I can start from book one to book seven but \i would simply be ranting and saying the same points over and over again so I will focus on Book six which really made we ask the Question above all others. In Book six we learn about the Hocruxes and we see through one of Dumbledore's memories and the climax of the book that these Hocruxes were not only well hidden but also magically powerfully protected. The protection around the ring alone almost killed Dumbledore and he himself points out that only a person of his skill could survive that curse. When He and Harry go to the cave, as Harry is watching Dumbledore he points out the fact that only a wizard as powerful Dumbledore could decipher the magic around the cave to not only find the door but penetrate the defenses. Putting book seven aside and looking at these points from a logical perspective, it follows logic that we are to assume or at least Dumbledore and Harry have to assume that Voldermort secured the rest of the Hocruxes in similar fashion.
Now Dumbledore knew that he was dying and that Harry had to finish the Job. Not only that but he also forbade Harry from telling anyone but Hermione and Ron about the Hocruxes meaning He intended for these three to go out and find the Hocruxes and Destroy them. Dumbledore knew all this but We never see him teach Harry any magic of how to detect the defenses and lift what ever curses guarding the Hocrux. He also knew that Harry was going to be hunted down hence chances are he was going to have to fight, and hide meaning he needed to know of more powerful defensive spells to help him fight and hide while on his mission. Given these points, to me it follows logic that if Dumbledore did not teach Harry or at least provide a protector then Dumbledore knew Harry was powerful enough to handle all the magical defenses around the Hocrux i.e. Harry was indeed a powerful wizard Otherwise if not then Why would Dumbledore send Harry on a mission that He knew Harry had no chance of survival. It is impossible for Dumbledore to have known exactly what harry was going to face and you cant say he knew there was going to be simple way to get the Hocruxes and didnt matter how powerful Harry was because Logically speaking all evidence pointed to defenses so powerful no ordinary wizard let alone a 17 year old kid could handle.
It is therefore Illogical for Harry not to be powerful because there is no way a weak or average wizard could survive the protective magic that would be protecting the Hocrux. For those that like to point to book seven and say Harry dint really need to be powerful to get the Hocruxes I need to remind you that Dumbledore and Harry never knew that all they knew was that the Hocruxes were out there and I think it prudent to Hope for the Best but prepare for the worst, not hope and prepare for the best. I actually think that Book seven was without a doubt the worst in the series and found it disappointing that it seemed like on every turn Voldermort and the Death eaters kept on blundering and giving Harry an advantage it almost seemed like every action Voldermort took would come back and bite him and every action harry took would in the long run prove profitable. before i go of point let me stop myself here I will write later about the plot holes in books 5 6 and 7 that again asks the Question of harry's power and the logic of it all.
In conclusion for the series to make sense, for Dumbledores decisions to make sense I cant see any other way but to conclude that Harry was an extremely powerful wizard whose power was not yet at its full potential and whose magical learn was still too litle but both were on the ascend and with time 10, 15 years harry would finally reach that level how ever he was powerful enough to at least fight the protection around the Hocrux if any.