Just because there is no explicit, direct link between The Sorcerer's Apprentice and the Dresden Files, doesn't mean that Butcher's novels didn't influence the movies writers and producers.
The Dresden Files are one of the most well known, widely read works of modern fantasy (sometimes called "urban fantasy"). As a result, the contents of the books have and will permeate the public meme space for many years to come.
Also, since the Butcher novels are some of the most well regarded novels of the genre, any work (such as The Sorcerer's Apprentice) that bears even the slightest or most superficial resemblance will inevitably be compared to the Dresden Files. While I enjoyed the movie very much, I must point out that with Rotten Tomato scores of 41/56, many people didn't like it as much as I.