Dresden can be more related to than Potter. Dresden lives in our world, he has an actual job, he interacts and behaves like any other human being. Potter on the other hand, lives in a separate world, very little we can relate to (Magical school, flying Ford cars, absurd sports). Potter himself, seems too self-important and he loves to save the day. His overbearing ego places him in situations not meant for normal teenager (but once again, who said he was normal) There is much growing up he has to do.

Dresden, relies on his magical abilities to live in our world. He has never attended any fancy school and was raised as an orphan. Dresden has morals and standards he lives by and doesn't care if he spits in the eyes of demon, gods or bitchy government authorities if he feels that it needs to be done. 

Physics in Dresden Files are more realistic and illustrative than in Potter's world. Throwing around spells should make you visibly tired since you are placing large amounts of energy and the strain that comes with it under your control.

Dresden, by majority is most related to our world and therefore possibly outclasses Potter.