The "Holy Thursday" to which Blake's poems refer is not Maundy Thursday, but Ascension Day, the celebration of Jesus's rise to heaven in his corporeal form. In the Anglican tradition, this festival is celebrated 39 days after Easter Sunday. Ascension Day observances at St Paul's Cathedral in London used to include a special service for children who attended charity schools. This special service ceased in 1941, both because the church had been damaged in the Blitz and because children had been evacuated from the city.
The poem in Songs of Innocence depicts this bygone service. The children in their school uniforms represent innocence. As another answer on Literature Stack Exchange says, innocence for Blake is not passive sweetness or ignorance, but a charged force. The power of the children's innocence is seen in their voices, which reach heaven:
Now like a mighty wind they raise to heaven the voice of song,
Or like harmonious thunderings the seats of heaven among.
Blake has repeatedly called the children a "multitude" and compared them to "Thames waters." He now associates them with forces of nature like "mighty wind" and "thunderings." He also emphasizes their affinity to Christ: through their voices, the children ascend to heaven, just as Christ is said to have done on this day. Both in the poem and in its illustration, it is telling that their patrons, the "wise guardians of the poor," are beneath the children (click the image for the full-size version):
In these ways, while the poem appears to celebrate charity, Blake shows that the recipients are mightier than the donors. The children's innocence is like a force of nature or like Christ, whose stainless innocence gave him tremendous power.
In Christian belief, humankind's fall from innocence corresponds with a knowledge of good and evil. The corresponding poem in Songs of Experience regards the children participating in the Holy Thursday rite from the point of view of not innocence, but experience: unlike them, the speaker is aware of the workings of evil in the world. The first stanza immediately announces that there is nothing "holy" about this exercise of charity, because the very existence of poor children in a wealthy society is an affront to the Christian ideal:
Is this a holy thing to see
In a rich and fruitful land,—
Babes reduced to misery,
Fed with cold and usurous hand?
What could be seen as philanthropy is exposed as evil, since it takes for granted the existence of suffering innocence. The children's song that reached heaven in the earlier poem is now recast:
Is that trembling cry a song?
Can it be a song of joy?
And so many children poor?
The force of the children's song still reaches heaven, but it is now a clarion call against corruption and injustice. Blake sees the ostentatious display of benevolence in the special service as morally bankrupt because in a just world, there would be no poverty and no need for largesse.
This answer is at variance with the claim in a different answer that the poem have "not much in common except the titles." Rather, both poems depict and comment on the same specific tradition associated with Holy Thursday, i.e., Ascension Day: the charity children's service at St Paul's. They dissect this service from the contrasted points of view of innocence and experience. The children are made analogous to Christ in their innocence, while the eye of experience portrays their supposed benefactors as hypocrites. Here as elsewhere, Blake uses the contrasted perspectives in his innocence/experience pairs to question accepted practices and overturn established hierarchies.
