1. Root Cause - Women
One of the main themes discussed in the Ramayana is the abduction of Seetha, the wife of Rama by the king of Lanka, Ravana. Its a very popular thought that Ravana was a villain but truth is that he was just acting as a dutiful brother - his sister Surpanaka was humiliated by Rama and she wanted revenge. If Ravana was a true villain he would have done something worse to Seetha than just lock her up in a garden. A women was the root cause of the war in Ramayana, the women being Surpanaka, not Seetha. And if we look further back what caused Rama to leave home but the fatal advice given by the humpback Mantara to Kaikeyi, Rama's step-mother.
In the Iliad, Helen the beautiful newly wed queen of Sparta falls in love with Paris, the prince of Troy. A story behind this is that he actually made Aphrodite, the goddess of love, put a spell on her in return for helping her(Aphrodite) win a bet against Hera and Athena. Helen 'runs away' with Paris to Troy. And what does Helen's husband, Menelaus do? He gathers the forces of Greece and attacks Troy, causing the Trojan War. Here too a women, rather a goddess is responsible for outbreak of war - not Helen, but Aphrodite.
In both cases, women are the root cause of the war.
2. Specialty of cities
This is a very interesting look at the two epics. The common point between Lanka and and Troy is that both were unreachable. The city of Lanka was and still is an island, miles away from any other piece of land. The sea between Lanka and Rameswaram(in India) was then infested with dangerous creatures and crossing that by boat would have been no picnic and not many boats could have taken a whole army across in such a short time. For this specific reason, a bridge that could enable a whole army to march on it was built with rocks.
Troy on the other hand had unbreakable walls. These walls were made by Gods - the wall was by legend built by immortals Poseidon and Apollo. Legend had it that you could only get in to Troy through invitation, which is what the Greeks so cunningly obtained through the Trojan Horse.
In both cases the cities were unreachable and it can also be noted that the bridge and the Trojan horse served the same purpose - breaching the unbreachable.
Ever read the Odyssey? The wanderings of Odysseus, the legendary king of Ithaca and mastermind behind the plan of the Horse, is very similar to the wanderings of Rama in his early years of exile.
These are just a few points, reading the Ramayana and the Iliad, we can find even more.
Now I am no conspiracy theorist and I'm just telling you the few similarities I noticed, thats all. Many conclusions can be drawn from the above - Homer copied Valmiki or the other way around, both were the same story but told in different versions, etc. I'll leave it to you to decide