Marlowe's poem is an idealized version of domesticity. He is using the beauty of nature to encourage a young woman to live with him and to be his lover. By using nature, Marlowe is asserting that this action is a natural thing, and is glorifying the sexual relationship as he glorifies the season and the natural surroundings. Marlowe is offering a relationship to this woman, and encouraging her in the language of romance. Although the promises being made and the pleasures being mentioned are sexual in nature, he is suggesting a real relationship.
Marvell isn't concerned with a relationship. Marvell is concerned with time. He is interested in the pleasure alone, and is suggesting to his mistress that life is too short to wait for a relationship to lead them to that inevitable coupling. He thinks that, because the two are growing old, they must make "sport... while we may." Marvell makes no promises to the woman, as Marlowe does, and is much more specific about what it is that he wants.
So to answer your question - yes, Marvell is more explicit in what he wants, and while Marlowe uses hyperbole to accentuate the beauty of the relationship, Marvell uses it for the purpose of persuasion only, and not for a relationship, but just for sex.