In my mind, this question is easily answered. <PERSON> is clearly the better wizard, and here is why.
<PERSON> is obviously a humble man, mostly due to mistakes made in his youth. On many occasions he says that people calling him "the most powerful wizard ever" are flattering him. But you'll notice that he does well to never tell untruths, he just bats around it. For example, in <PERSON> answer, the conversation with <PERSON>, "He had powers I will never have". This is true because <PERSON> had Horcruxes and the use of Inferi, but <PERSON> doesn't say, "<PERSON> would have beaten my pants off in a duel!" Because he knows he is more powerful than <PERSON>.
Next, let's look at some quasi-quantitative data. Duels! Let's look at the fights we see <PERSON> win. He defeats <PERSON> at the height of his power against the power of the Elder wand. This takes some doing, but we don't know that <PERSON> couldn't have achieved the same feat. We see <PERSON> defeat four ministry of magic officials in one 10 second duel, 3 if you don't count <PERSON>. And, possibly most importantly, he finishes the duel at the Ministry between the death-eaters and the order. All of the death eaters, who are claimed in the book to be almost as bad as <PERSON> himself, flee before him, and he rounds them up with very little effort. <PERSON> meanwhile, confronts, at most, two at a time. <PERSON>'s unarmed parents, Madam <PERSON>, <PERSON>. Basically, <PERSON> just kills one on one, and normally against the unarmed, although, it is possible he has killed a ton at once, but even this takes little skill. The Avada Kedavra is only one spell. The only time we see him have a real challenge is during the battle of Hogwarts where he duels three at once, <PERSON>, <PERSON>, and <PERSON>(?). 773
He fails to kill any of these three, although he is not overcome by them. Of course this is hard to put definitively, but I would tend to give <PERSON> the edge here.
Speaking of the Duel at the Ministry, let's look at the duel between <PERSON> and <PERSON>, their only face-to-face battle, as far as the books tell us. <PERSON> is doing his best to defeat <PERSON>, while <PERSON> knows killing <PERSON> is useless. He seemingly has <PERSON> defeated after encasing him in water, before <PERSON> possesses <PERSON>, then runs away. All the while <PERSON> is charming the statues of the Fountain of Magical brethren to keep them protecting <PERSON>. Now, it isn't clear exactly who is actually superior. <PERSON> is not truly trying to kill <PERSON>, as he knows it's useless, so he may be trying to capture him alive, or gain information about the suspected horcruxes, which would imply that he is not giving it his all, however, he also possesses the Elder wand during this fight, and <PERSON> takes a curse which seems to be lethal, so <PERSON> is not fighting on pure skill. It seems as thought <PERSON> had the upper hand to me, however.
Honestly, I think the most damning evidence is schoolwork. Yes, it may seem underwhelming, but think about the description of the two wizards at school. We have <PERSON>, the quiet but talented boy who charmed all his teachers. He received top marks in every subject and the award for special services to the school. You know who else scored top marks in every subject? <PERSON>, the constantly confunded Auror, who is one of the ministry officials <PERSON> owns. And that award for special services? He arrested the wrong person, who put up no known struggle, for a crime he committed. What a talented young lad. <PERSON>? According to <PERSON>, he won EVERY prize of note at the school, was published in many research journals including 'Challenges in Charming' and 'Transfiguration Today', aced all his NEWTs, and was soon in correspondence with the most noted magical researchers of the day including <PERSON>, a man who was already hundreds of years old at the time, yet needed the help of a 17 year-old-boy. YEAH, he was talented as no one else ever was. You can try to excuse this by the old, "yeah, but <PERSON> didn't try at school", except that he did. 773