This is a really good story. The combat scenes of the first chapter were excellent and the incredible introduction of Harry into the Dresden-verse world was excellently done. It almost felt like a passage taken from the books.
So far I can tell, the HP-world's magic is significantly more powerful and versatile on a small scale. They don't have all these ancient destroy-the-world runic circles and such, but their wand magic seems to pack a significantly greater punch, not to mention that HP mages appears to have access to an infinitely greater repertoire of different kinds of spells.
As for wand magic vs these blaster staffs... No contest. One just need to take a look at all the different ways HP mages have of killing and maiming things. The ever-cutting curse, Sectumsempra and the ultimate fire spell, Fiendfyre comes to mind.
With that said, I believe poor Harry will have a very hard time convincing people that, no, he's not an evil soulless demon from the Outside and that, no, he isn't here to conquer, destroy or generally fuck up peoples lives.
It'd be fun to have him square off against a minor Denarian and kick up an ant's nest...
Author's response
Thanks! HP magic is indeed significantly more versatile, but Dresden magic does have its own strengths. I don't know which one is more powerful. About Denarians, I'm not sure if I will use them, but yeah, it would be highly interesting to see Harry fight one.