In the 28 BCP the priest alone says the prayer of Humble Access. In the 2019 the priest and the congregation say the Prayer of Humble Access. Is there a theological reason behind the changes or does it not really matter?
1928 follows the practice of 1662 Then shall the Priest, kneeling down at the Lord's Table, say in the name of all them that shall receive the Communion this Prayer following. WE do not presume to come to this thy Table, O merciful Lord, trusting in our own righteousness, but in thy manifold and great mercies. We are not worthy so much as to gather up the crumbs under thy Table. But thou art the same Lord, whose property is always to have mercy: Grant us therefore, gracious Lord, so to eat the flesh of thy dear Son Jesus Christ, and to drink his blood, that our sinful bodies may be made clean by his body, and our souls washed through his most precious blood, and that we may evermore dwell in him, and he in us. Amen. When you look at the rubric, it seems clearly intentional that the priest is speaking for Priest and People at this time, so it seems to make sense that all the congregation might say this prayer together with the priest. I think it is a question of liturgical practice rather than of theology. I am not sure what the rubric said in 1928.
The rubric is identical in the 1928. In practice, this came to be a prayer that was said in unison. I have seen very few parishes where the people do not recite this prayer with the celebrant. Humble Access is one of the vestiges of the Anglican communion service that the Romans have allowed Ordinariate parishes to retain. It is prefaced with this rubric: "Then the Priest, bowing profoundly, says with all who shall receive Communion."
I have a feeling that the origins of the Prayer of Humble Access go back to the Pre-Norman Conquest English Church, together with the Collect for Purity.
Massey Shepherd, an American prayer book scholar of the 20th century, wrote that Humble Access was an original composition of Archbishop Cranmer but he drew inspiration from the liturgy of St. Basil and some medieval Collects. The prayer first took on its present name in the Scottish liturgy of 1637.
I have heard it said that there was a desire among (some) lay people to have a more active voice in the Eucharistic canon, and the Prayer of Humble Access was one prayer that was considered appropriate for all to join in for. But then again, I was first taught Prayer Book stuff by slightly-liberal episcopalians who loved the 1979 Book, so they might have been biased. Whateverso, I agree with the comment above that there is likely no theological significance to adding the people to the recitation of that prayer. What might be more theologically interesting to explore is where in the liturgy different Prayer Book place it I began to explore that last year: https://saint-aelfric-customary.org/2019/11/07/the-prayer-of-humble-access/