Three important elements that these poems share are allusions to Greek mythology, flowery diction, and a first-person perspective.
Bradstreet compares her own poetry to that of the Ancient Greeks and notes that the Greeks made the Muses female, therefore being more lenient towards women than people of her own era. Milton uses extensive classical allusions to describe how the speaker can benefit from melancholy.
Both poems use extremely flowery diction, which is to say that they say what they have to say in unnecessarily complex and pretty ways. For example, Bradstreet calls on "oh ye high flown quills that soar the skies," while Milton refers to "him that yon soars on golden wing." However, Milton's diction is more consistently flowery throughout than is Bradstreet's.
Finally, both poems use the first person, perhaps suggesting that the speaker is Bradstreet or Milton, respectively. Bradstreet's speaker is explicitly a woman writing about writing poems, while Milton's poem refers less directly to his personal identity.