Since the Aeneid is the national epic of Rome, written with the Homeric epics in mind as both models and competitors, almost any episode in the poem can be compared with the Odyssey. The opening lines of both epics, in particular, emphasize the exceptional man who is the hero and the dangers he will face on his voyage from Troy. Virgil implicitly compares Aeneas to Odysseus, though he is to have a longer journey and a nobler mission. He is not merely returning home, but fulfilling the will of the gods in founding a new city, which will grow into the greatest empire the world has ever seen.
Although it is an epic in form and structure, the Aeneid clearly has passages of tragedy, notably in book 4 when the love affair between Dido and Aeneas comes into conflict with the will of the gods, leading to Dido's death. This was later a popular subject for works of tragedy, such as Henry Purcell's opera, Dido and Aeneas.
The Aeneid contains almost no comedy and certainly no Aristophanic comedy. Augustus, Virgil's patron, would not have approved of the vulgar sexual comedy of Aristophanes. The poet who comes closest to writing like this (and even then, not very close) is Ovid, whom the Emperor famously banished. There are moments of dark humor in the Aeneid, such as the episode in book 10 where Virgil remarks that the parents of the twins Thymber and Larides have difficulty in telling them apart. This, however, will not be a problem in the future, since Pallas cuts the head off one and a hand off the other. The hand that has been cut off twitches, and Virgil remarks that it is groping for its sword. This is as close to comedy as the Aeneid ever gets, and it is not remotely similar to Aristophanes.