Varaali My memory is faint, but I recall reading about Paris being asked to adjudicate some contest b/w Hera, Athena and Aphrodite. All 3 tried to influence his decision w/ promises of gifts - Hera promised him power, Athena wealth, and Aphrodite the most beautiful woman in the world. Paris judged Aphrodite the winner, which made Hera and Athena the enemy of the Trojans. Also, the woman who Aphrodite had promised him was Helen. It's interesting that she didn't promise him the most beautiful maiden in the world, but most beautiful woman, period.
In the Ramayan, Sita, in her previous birth as Vedavati, was harassed by Ravan, and vowed to get reborn to cause his death. So in other words, Paris was promised Helen as a gift from someone who wanted to reward him, whereas Ravan was promised that Vedavati would be reborn to cause his death. That too is a pretty big change in circumstances.
In the Ramayan, the logical sequence made sense - as long as Ravan was alive, there was no question of releasing Sita, and as long as Ravan's kinsmen - Indrajit, Kumbhakarna, Atikaya, Prahast, Kumbha, Nikumbha and others were alive, it was impossible to kill him, thereby making the war last until the death. I think that had Rama killed Ravana on their first encounter, leaving Kumbhakarna and Indrajit alive, there are some chances that the war might have ended, although Indrajit, as a potential successor, may have chosen to continue the war with or without returning Sita. But point is that aside from Ravan, nobody else was interested in Sita - not Indrajit, not Kumbhakarna and not anyone else. The other thing here was that since Ravan was the king, his decree to have Sita ruled, and nobody could overrule him.
With the Trojans, it didn't, since after Paris died, Helen remained w/ the Trojans until Troy fell. Frankly, I haven't heard the story of her moving on to any of Paris' brothers, so I too would have to read up on that aspect. But unlike in the Ramayan, after a number of years where leading warriors on both sides - Patrocleus, Hector, Achilles were killed, the war acquired a momentum all its own, and at this point, it was a war to wipe out the other side. Normally, Prium might have overruled Paris and returned Helen, but nothing like it happened. In the Ramayan, Rama was pretty happy to accept Vibhishan and name him as the future ruler of Lanka. Here, had any Trojan gone over to the Greek side, it's unlikely that they'd have decided to exempt the Trojans from a massacre. In other words, this was a deathmatch war b/w the Greeks and the Trojans.
This momentum issue also showed itself up in the Kurukshetra war as well. After a number of warriors on both sides were killed, ending the war was pretty much out of the question. There was no way that Duryodhan was going to call off the war after the fall/deaths of Bheeshma, Lakshmana, Jayadrath, Drona, Dushashan, Karna and Shakuni, and just as unlikely, Yudhisthir wouldn't have called off the war after the deaths of Uttar, Sveta, Sankha, Satyaki's sons, Iravana, Drupada's various sons, Abhimanyu, Kuntibhoj, Dhrishtaketu, Sahadev of Magadha, Drupada, Virata and others. Doing so would have just illustrated that those people died in vain, so only a victory would vindicate their heroism. The same logic ran w/ the Greeks and Trojans. In fact, w/ Ravan too, once several leading kinsmen, including Kumbhakarna & Indrajit were killed, it was impossible for him to accept any peace, since even if it didn't demonstrate him as a coward, it would certainly have made the point that they died for nothing.