Is Doctor Faustus a morality play or a Renaissance drama?

Doctor Faustus is both a morality play and a Renaissance drama, since the two are not mutually exclusive categories of drama. The play shows a man selling his own soul for power when all the normal sciences cannot satisfy his quest for knowledge, and the power does not make him a wiser man, but a more foolish and proud one—therefore, it is a morality play. It also deals with Renaissance era themes—man's reaching for knowledge, questioning the superiority of man—and features many of the hallmarks of Renaissance-era tragedies (such as a character's downfall coming from a fatal flaw and their own psychology rather than from fate or God's will, as in medieval tragedy).
However, some have wondered about the theological implications of the play and how this relates to its categorization as a morality story, particularly since Marlowe is believed to have been an atheist with no big love for the organized church. Is Faustus tragic because he reached too far and this is wrong, or is he tragic because he was wrongly killed for seeking to reach beyond human limitations at all?
Judging by how Faustus wastes his powers with jokes and tricks, I would say Marlowe's interests are in presenting a morality story condemning such reaching, but not every reader has agreed and it is very much up for debate whether it is a straightforward morality play or a more subversive one.

It's both, and the two are closely linked together. Doctor Faustus is a morality play in that it shows us the dangers of selling your soul to the devil. That's precisely what the title character does, hoping that it will bring him magical powers with which he will gain control over the world. And it is Faustus's insatiable desire for knowledge that also makes Marlowe's masterpiece a classic example of Renaissance drama.
The Renaissance was a time when whole new vistas of knowledge opened up for Western Europeans with the rediscovery of ancient learning. With the possession of this knowledge often went a certain arrogance, a sense that man could do almost anything if only he put his mind to it. Like so many of his contemporaries, Faustus comes to realize to his cost that this isn't true; that there's a limit to human knowledge and that it simply isn't possible or desirable for man to know everything.