The Rambam paskens (Hil Brachos ch 5) that a child as an obligation in birchas hamazon based on the din of chinuch. A child can be motzi an adult who ate less than k'dei sevi'a (i.e. the adult's chiyuv is also only derabannan) because the child's obligation is parallel to that of the adult. Yet, in Hil Chanukah (ch 3) the Rambam states unequivocally that a child cannot be motzi an adult in kri'as hallel even through the Rambam holds that kri'as hallel is only a chiyuv derabbanan.
Once upon a time we discussed the machlokes Rishonim whether chinuch is an obligation on the father to train his son, or whether it makes the child chayav m'derabbanan in mitzvos. It's beyond what I have time now to get into, but it seems the Rambam formulates it different ways in different places, sometimes writing "mechanchin es ha'katan" (or other such terminology), indicating the obligation rests on the parent, other times, like with respect to bentching, indicating that the katan himself is obligated in the mitzvah. Whether there is any distinction in this regard between bentching and mikra megillah is something worth looking into.
Rav Wahrman z"l in his sefer She'eiris Yosef (vol 7) offers a different distinction, one that we discussed before as well. R' Shternbruch (see full post here) is mechadesh that chinuch only obligates a child in mikra megillah but not in the seudah of Purim. The difference between the two is that mikra megillah is a mechanical act; the reading is an end in and of itself. The seudah of Purim is a means to fulfill the mitzvah of simcha, which is an emotional state. The kiyum b'lev is the essential component of the mitzvah. A child may not understand fully what he/she is doing, but he/she can perform a behavior; however, when the emotions and thoughts are themselves part and parcel of the definition of the mitzvah, the katan has no way to do the mitzvah properly.
Hallel, suggests R' Wahrman, is by definition a reflection and expression of simcha. Without that kiyum b'lev, it's just words. That's why on Rosh haShana and Yom Kippur, where, as the gemara says, "the books of life and death are open," we are exempt from hallel. The recitation would be devoid of the joy that makes the reading into hallel. A child cannot empathize and feel the same emotional response as an adult; therefore, there is no chinuch on the mitzvah of hallel.