Bill Bryson has a rather nice passage in his biography of Shakespeare which I thought I might quote:
"[In 1593] Shakespeare was writing comparative trifles -
Love's Labour's Lost, The Two Gentlemen of Verona and
The Comedy of Errors are all probably among his works of this period. Marlowe by contrast had written ambitious and appreciable dramas:
The Jew of Malta, The Tragical History of Doctor Faustus and
Tamburlaine the Great. 'If Shakespeare too had died in that year,' Stanley Wells has written, 'we should now regard Marlowe as the greater writer.'
"No doubt. But what if both had lived? Could either have sustained the competition? Shakespeare, it seems fair to say, had more promise for the long term. Marlowe possessed little gift for comedy and none at all, that we can see, for creating strong female roles - areas where Shakespeare shone. Above all it is impossible to imagine a person as quick to violence and as erratic in temperament as Christopher Marlowe reaching a wise and productive middle age. Shakespeare had a disposition built for the long haul."
Still, he's already generally recognised as the number two Elizabethan dramatist- unless he manages to unseat Shakespeare he's still going to be number 2 even if he does survive.
My own limited experience has been that Jonson tends to be regarded as the number two rather than Marlowe.