The answer to your question concerning these two carpe diem poems is probably a matter of opinion, and probably is determined by the values and ideas a reader brings to the poems.
Marvell wants to sleep with his lover. Herrick is giving advice to women to marry while they are young so they can find good matches or avoid not finding a match at all.
I think which poem is seen as more successfully persuasive depends on what one thinks of sex and marriage. Certainly, a woman absolutely against sex outside of marriage would probably not be persuaded by Marvell's rationalizations, for instance.
At the same time, one should remember that these metaphysical poets, as we call them today, are having fun with their poems. The style and the stretched metaphors and unusual imagery are humorous and entertaining. I mean, really, how serious are we supposed to take "vegetable love"?
I don't know which is more persuasive, exactly, but I think that Marvell's poem is more powerful, which is probably the same thing.
I think that Herrick's poem is way more subtle than Marvell's. It does talk about life being fleeting, but in a pretty subdued way. It says that the higher the sun gets, the nearer it is to setting, for example. That's not a very stark metaphor.
Contrast that with how explicit Marvell is. He's talking about his mistress's beauty being locked away in a tomb and worms "trying" her virginity. That's so much more "in your face" of an image.
So if you like subtle, Herrick is more persuasive. If you like powerful scare tactics, Marvell is.
I am not sure if you could say one is more persuasive than the other, since both were masters of the language they used. Who is more persuasive, Shakespeare or Chaucer? What the poems have in common is a similar motif--they are both carpe diem poems which implore to make the most out of time, and they both have the same logical argument, it can be said that it is a softer, more gentler tone, though Herrick shifts the emphasis to "you" in the final stanza.
Herrick's "dying" and "setting" are completely offset by "gather", "smile", and "run". There is almost a grandfatherly advice feel to it. Whereas Marvell is much more self-centered on the speaker's pleasure, and his "sun" races through the sky. Herrick's is much slower and gentler.