"What are your favorite books?"
Translation:Quels sont tes livres préférés ?
From what I have read they both mean favorite. However, favoris is less common and more "old fashioned" sounding. Of course, that could be something one is going for, depending on the situation. I found this: https://answers.yahoo.com/question/index?qid=20071011230457AABYCYI and this: https://hinative.com/fr-FR/questions/280 I'm still learning as well, but hope that helps. :)
Quels is used here because it is the plural masculine form to go with the plural masculine livres. It would be quel if referring to one book, or quelle if referring to a feminine word, such as la soupe. Or Quelles if more than one. (les soupes)