Hallel

On the Yom Tov of Pesach we only recite full Hallel on the first days. After that we recite only a chatzi hallel. On Succos this is not the case. Rather, on Succos we recite a full hallel the entire Yom Tov.

Why the distinction?

There are two reasons given for this. The gemara in Erchin on 10a/b says that on Succos there is a different korban every day. Therefore each day is like an independant Yom Tov and deserves its own full Hallel.

The Midrash gives a different reason. The Midrash asks why don't we say a full hallel on the 7th day of Pesach? After all, weren't the Jews saved at the Yam Suf?

The Midrash answers with the Pasuk of Binfol Oyvecha Al Tismach... Maasei Yadi Tovim Bayam V'Atem Omrim Shira? In other words, we don't say hallel on the downfall of Hashem's creations.

Rav Aharon Kotler explains the necessity for two separate reasons. There are in fact two separate michayvim for hallel. One mechayev is Yom Tov. Since Pesach is all one Yom Tov there is no need for a full hallel every day. Succos, on the other hand, is a new Yom Tov every day because of the different Parei HaChag, the different korbanos of each day.

The other mechayev of hallel is nes. We say hallel any day that a miracle occured to Klal Yisroel. Thus, the midrash asks, even if the 7th day of Pesach is not a Yom Tov independantly, perhaps the nes of the Yam Suf should be mechayev hallel? To which the midrash responds that this is not the case because this nes also represents the downfall of God's creations.