Q. In a recent answer you explained that one reason why Hallel is not said on Purim is that the Megillah is in itself a praise of God. Could we not say that the Haggadah is also a praise of God, so why is Hallel said on Seder night?
A. This question is addressed by Rav Soloveitchik in his “Reflections of the Rav”, ed. AR Besdin, 1977, ch. 20.
He argues that shevach (praise of God) is not the whole purpose of the Haggadah. Instead, “We are expected to rise to higher levels of exultant praise, to a shirah chadashah (a new song)… We ecstatically see all of creation joining in a grand symphony of homage to God for all the blessings of life…
“The concluding note of the Haggadah is an eschatological vision of a glorious future, when ‘every mouth shall give thanks and every tongue swear allegiance unto You; every knee shall bow to You’. To highlight this added dimension of gratitude, the Hallel and the Hallel HaGadol (Psalm 136) were included in the Haggadah” (page 216).