Use the adjective emulous to describe someone who tries to imitate or copy another person. An emulous student might both admire and feel jealous of the teacher he imitates.
When you're emulous of a friend, you feel a bit competitive, wanting to do what she does, and to do it better. Younger siblings are sometimes emulous of older brothers or sisters, and art school students might be emulous of established, working artists. When you want to be just like someone, you're emulous, and when you want to surpass that person, you're also emulous. The Latin root is aemulari, "to rival."