She doesn't prefer either one of them to the other. The title tells you that she loves them both "equally". She says that Damon would never had gotten her heart if Alexis had not come along. But then again Alexis could not gain her love if it hadn't been for Damon. When Alexis is present, she wants Damon; but when Alexis is absent, Damon gets nothing but her scorn. She can't make up her mind, so she asks Cupid to take back one of his darts and do it for her. However, she starts to reneg on that request because if Cupid would pick Damon, all her hopes would be dashed; but if Cupid picked Alexis, she would feel lost.
"On Her Loving Two Equally" by Aphra Behn is a humorous poem describing the situation of a narrator who rather likes having multiple admirers. This isn't a poem about a deep, serious romance, but rather about a narrator who likes flirting and attention and really doesn't want to give up either Alexis or Damon.
One of the ways we know that this poem is meant as lighthearted is that the narrator says that when she is in the company of Damon, she thinks of Alexis and:
When my Alexis present is,
Then I for Damon sigh and mourn;
In other words, she is really not deeply in love with either of the two men, but enjoys being courted by both of them. The final stanza emphasizes that she really doesn't want a deeper relationship with just one of the two, but rather she just enjoys playing them off against each other. This is why the title is "On Her Loving Two Equally"; neither of the two is favored over the other.