Shakespeare's "Venus and Adonis" is a work that displays technical mastery and flare more than it makes a statement or conveys a message about the nature of love. In Shakespeare's time, great poetry was regarded as the height of literary accomplishment (unlike plays, which, for all their popularity, didn't usually win their authors literary prestige). "Venus and Adonis" was Shakespeare's first published poem—it was his declaration that he had the capacity to be a serious author (not just a playwright). As such, the poem showcases Shakespeare's technical abilities as a poet; it is "a storehouse of the rhetorical figures and imagistic techniques of Elizabethan lyric style," in which "balance and antithesis, alliteration and assonance, produce a pleasing aural effect not so much to underline the meaning as to call attention to their own beauty" (eNotes).
In short, it's a little tough to figure out how Shakespeare's trying to portray love in "Venus and Adonis" since it doesn't seem like painting a portrait or making a statement about the nature of love is his first priority. That said, we can look at the different ideas of love that Venus and Adonis have (and perhaps represent), even if we can't really draw a conclusion about which one wins out over the other.
Venus is all about physical love; she physically pulls Adonis from his horse, pushes him backwards, and interrupts him with kisses (as eloquently as she speaks, these seem to be a significant tool in her persuasive arsenal). Her desire makes her "red and hot as coals of glowing fire." She also hints (and mythology confirms) that she's had many lovers—further emphasizing her understanding of love as transitory and physical. She describes her physical appearance ("My beauty as the spring doth yearly grow, / My flesh is soft and plump, my marrow burning"), and points out that no one will know what they've done.
Adonis, in contrast, is "red for shame, but frosty in desire"—he doesn't at all want Venus's kisses, and would really like to get back to his hunt. He chastises Venus for being improper ("He saith she is immodest, blames her 'miss"), and remains "obdurate, flinty, hard as steel, / Nay, more than flint, for stone at rain relenteth." Adonis might represent rational control over physical desire (mind over matter)—though it's difficult to say since he doesn't actually feel desire for Venus; he isn't remotely tempted. Adonis is interested only in enduring, faithful love; he doesn't like that Venus "lends embracements unto every stranger," and says "I hate not love, but your device in love." He prefers heavenly love to physical lust: "Call it not love, for Love to heaven is fled, / Since sweating Lust on earth usurp'd his name."
The end of the poem doesn't really let either perspective of love triumph over the other. Adonis dies and Venus mourns beautifully—neither wins.