The nightingale describes the student who needs the red rose for his "true love" as follows:
His hair is dark as the hyacinth-blossom, and his lips are red as the rose of his desire; but passion has made his face like pale ivory, and sorrow has set her seal upon his brow
The student is also described as one with "beautiful eyes". However, this is his direct characterization. We can characterize him indirectly by looking at his behavior, as well as at the things that he does throughout the story, to make a good profile of what he is like. Unfortunately for the student, his physical beauty is simply that: physical. There is very little of that beauty in the person within.
First, he is shallow. He wanted to impress a girl with the flower only to take that great sacrifice that it later on became and toss it out carelessly once the girl rejected him. He has a swollen ego because he could not take the girl's rejection. He is whiny and he only claims to have a "true love". He knows nothing of it, and he especially knows nothing of what sacrifice is. He is ungrateful, as he does not even care that the flower was a rarity. He is simply quite ugly.
The nightingale, as a bird, has nothing salient about her. She is described as "swift", but indirectly, she can be described with much more detail. She is a true believer of love. She is altruistic as she is willing to sacrifice her own life for the rose. She loves and she appreciates. She is thankful and grateful to all things in nature. Moreover, she is willing to die for what she believes. This may be somewhat brutal, but denotes the true desire to believe in something that you can live and die for.
It is very sad that the student could not understand that the song of the Nightingale was her telling him that he would have her rose, as she will pinch her own heart against the thorn of a white rose to make it red with her own blood.