The reunion of father and son in Homer's Odyssey is an emotionally touching scene and this question could refer to at least two instances I recall.
One reunion between father and son comes in Odyssey 24, where Odysseus is reunited with his father Laertes. Homer does not use a simile in this instance, though, so I shall assume that the questioner refers to another instance earlier in the epic.
This instance comes in Odyssey 16 and involves Odysseus' reunion with his son Telemachus, whom he last saw when he was an infant. Now Telemachus is a grown man, at least 20 years old. Homer compares the tears and emotional outcries of the two men as comparable to "birds of prey" who have been robbed of their young chicks.
Homer frequently compares human activity to activities of animals. For all the nobility of Odysseus and Telemachus, it is curious that Homer does not compare them to more attractive animals, but rather "vultures or sea-eagles." It is striking, though, that he does compare them to "birds of prey", since Odysseus and Telemachus will soon be involved in a bloody assault upon Penelope's suitors.