During chol ha-moed (intermediate days) of Sukkot we recite a full Hallel but during chol ha-moed of Pesach (and also Rosh Chodesh and some other days) we recite a "half Hallel" (really more like 85% hallel). Sukkot and Pesach are both chagim (festivals) and so I would naively expect them to have the same liturgical status. Why the difference? I can think of a couple possibilities:
An unanswered question suggests that Pesach Hallel is restricted because of the fallen Egyptians (according to the Shibolet Haleket, whoever that is). But, as noted in that question, we don't do that for the festival (chag) days in Pesach, which seems unusual if that's the reason. Also, if this is the reason, is there a different reason for reducing the Rosh Chodesh Hallel?1
Perhaps chol ha-moed "should" have the reduced Hallel for both, but Sukkot is zman simchateinu (the time of our rejoicing) so we increase our joy by increasing Hallel. I've never heard anybody make that argument; I'm just guessing here.
Can anybody provide a sourced explanation for why Hallel varies between the two chol ha-moed periods? If along the way an answer also explains why Rosh Chodesh is treated the way it is that'd be great, though my primary question is about the chagim.
1 Except in Chanukah, according to the siddur I used this morning. I might ask a separate question about that.