Can you perceive a continuity between Hector or Achilles from Homer's Iliad and Aeneas from Virgil's Aeneid?

There's certainly a degree of continuity between them as they're all incredibly strong, heroic warriors. At the same time, their bravery manifests itself in a myriad of different ways. Aeneas has been given a divine mission: to establish the great city of Rome. This is an onerous responsibility indeed; Aeneas embarks upon his epic journey, not for guts or glory, but because the gods have so ordained it. At various stages on his journey, not least in his abandonment of Dido, he has to suppress his own wants and desires for the greater good. Aeneas' heroism is heroism with a purpose.
Hector also has a sense of fighting for a higher, nobler good. He, too, is most certainly a brave warrior, but he fights because he needs to, not because he wants to. He knows that if the Achaeans prevail, the consequences for the Trojans will be disastrous. Not only will Troy be razed to the ground, but every last adult male will be killed and their children and womenfolk taken into captivity as slaves. Even so, Hector does everything he can to minimize battlefield casualties among his men. He never succumbs to a desperate craving for blood-lust or revenge.
Then there's Achilles. As a warrior he's in a class all of his own. No one seriously doubts his immense physical courage (nor would anyone dare to). And his skill on the battlefield is without parallel. In the intense heat of conflict he truly is the best of the Achaeans. That said, for Achilles it's all about number one. He sulks in his tent while his comrades are being systematically slaughtered, and all because Agamemnon commandeered his sex slave. Unlike Aeneas and Hector he has no concept of fighting for a higher purpose. Everything he does is for his own glory, his own elevated sense of pride. He only returns to the conflict after his close friend and comrade-in-arms Patroclus has been killed by Hector. Achilles takes this as a personal affront, and so his final duel with Hector is the settling of a vendetta. Right up until the end it's all about him.