In the two poems, "The Passionate Shepherd to his Love" by Christopher Marlowe and "The Nymph's Reply to the Shepherd" by Sir Walter Raleigh, who makes the best case?
I'm afraid who makes the "best" or better case between "Shepherd" and "Nymph" is mostly a matter of opinion, and one's opinion is mostly dependent on the attitude one brings to the question.
"Shepherd" is idealistic, while the response poem "Nymph" is realistic or cynical. I, for instance, tend to be realistic or cynical, so I prefer the argument in "Nymph."
The speaker in "Shepherd" considers "beds of roses" an offering that might convince his love to come live with him. The Nymph thinks only about the fact that flowers "do fade" and "wither." The former centers on youth and young love and the carpe diem (sieze the day) idea. The latter sees that youth ages and joy ends.
Both poems are respected enough to make it into the canon and appear in text book after text book, so both do what they do well. Which you choose as doing it better is up to you.
Perhaps your own age will determine your opinion. I have a hunch that I might have preferred "Shepherd" when I was much younger.