Aragon is similar to Aeneas in that he too will be founding and ruling a new country, one that brings forth peace during a time of civil unrest. Both men sacrifice much of themselves in order to fulfill a destiny and to better serve the people. Additionally, both men are making up for a failure on the part of their ancestors. The part of the movie that brought this to my attention was when Aragon was speaking with the father (i cannot remember his name for the life of me) in the tent before the battle. The father tells him that he may have hope and Aragon responds, basically saying that he saves his hope for the people not for himself.
It is also interesting that the two characters share a similar motif, fathers and sons. Aragon is fatherless and his ancestor has caused all of Middle Earth to suffer. This scene with a surrogate father reminds me of Aeneas and Evander. Advice is given by both father figures who are unable to join in the battle.
Lastly, both men receive special weapons made by magical figures for their battle. I am sure that the list of coincidences could go on forever, but my point is that Aragon is more of a Virgilian hero; he sacrifices everything for his cause and never seeks fame. Moreover, he is a humble servant of the people, who just so happens to wield a heavy sword.