Harry Potter with its fun and school references has magical power reside in wand form and Latin pronunciation, as well as knowing the right Latin. Magic corresponds to a number of classes much like Muggle school. In the later books magic also has mystical origins that come from deep relationship and character. Harry is protected by the love of his mother; Voldemort is protected by his willingness to divide his own soul. Still, it should be said that the Potter books have one of the least sensible, or explained, magic. In some sense this fits the books though, which are endlessly full of possibility, and at some points logic and system limits the multiplication of the fantastical.
Ursula Le Guin, in her Wizard of Earthsea created the most resonant magical system. In it, magic is the power to speak with creatures and objects by their true names. This relates to the knowledge of Tolkien but it has a clear line with both science, in which true knowledge of a thing allows humans to garner energy from it, and poetry, the idea that language is power.
The Name of the Wind is a new book that builds on Le Guin, but creates a complexity, with multiple branches of study. It would not be a stretch to say that Patrick Rothfuss wrote out a desire to take what is good in Potter and The Wizard of Earthsea and create the best magical system there is. One critique of his magic though would be that it, like Harry Potter, is about study and skill, but it also has no origins so it offers no explanation as to where the power comes for, or worse, asserts that the only meaningful power is one's self.
