Why do we say a full Hallel on all eight days of Hanukka, but only a half Hallel on the last six days of Pesach?
All sorts of answers have been suggested, but the simplest one is this:
We know from the book of Maccabees that Hanukkah was first conceived as a replacement for Sukkot. Vestiges of this origin remain. For instance, Bet Shamai wanted the Hanukkah candles to be lit in descending order in intimation of the Sukkot order of sacrifice. Maccabees also tells us that lulavim were taken at the first Hanukkah and that "hymns of praise" were said. Those hymns, perhaps, were Hallel, and perhaps the authorities of the time, in imitation of our practice on Sukkot, called for a full Hallel.
So perhaps that's why we say a full Hallel on Hanukkah.
Meanwhile, the Pesach liturgy developed on its own, based on other considerations. Some say we have a half-Hallel on the last days of Pesach based on the story of God silencing the angels. As you may remember, He told them not to sing during the Splitting of the Sea, so now we abridge our celebration as well. Others say the Hallel is abridged because the musaf service doesn't change on the last six days of Pesach. There may be other explanations, too.
The error, I think, is in assuming that there is some Rule of Hallel that can explain why Hanukkah gets a full Hallel when the last days of Pesach do not. I don't believe such a rule exists. The Sages never sat around a wisdom table establishing liturgies (though they did write individual prayers) The liturgies developed slowly over time, and were codified into law after they were already accepted by the people. One set of considerations can explains the full Hallel on Hanukkah while another set of considerations explains the half-Hallel on Pesach. There's no reason to think - on insist - that these two sets of considerations should be reconciled with one another.
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