There are no dependent clauses in that sentence. Both "Vampire Diaries is my favorite show" and "I also love True Blood" are independent clauses because they contain a subject and a verb, and could stand alone as a sentence. "but" is a coordinating conjunction that joins the clauses, meaning both are still independent. The coordinating conjunctions are For, And, Nor, But, Or, Yet, and So ("FANBOYS"). If a subordinating conjunction (such as "although" or "however") were to join the clauses, the clause containing the conjunction would be the dependent.
