The concept of one 'eating' another has several possibilities :
cannibalism : when one species eats another of its own species.
metaphor : one concept is used in place of another.
symbolism : one material thing represents another material thing.
spiritualisation : something spiritual is represented in material terms.
supernaturalism : one material is miraculously transformed into another
Cannibalism is mentioned in scripture, as in Jeremiah 19:9.
In metaphor, God says that certain adversaries 'eat up' his people 'like bread', Psalm 14:4 ; Paul says that certain brethren should beware lest they 'devour one another', Galatians 5:15 and Peter warns that the Adversary seeks 'whom he may devour', 1 Peter 5:8.
Symbolically, Jesus took a loaf, broke it and offered it, saying 'this is my body' whilst yet his body was intact and whole in front of them. Clearly, the loaf signifies a body and its breaking symbolises the future rending of Jesus' body. Thus the 'eating' must be symbolic also.
Spiritually, the epistles teach that a believer 'partakes' of the Christ, by faith and in the Holy Spirit, and is unified with Christ in his death, his resurrection, his ascension and his enthronement, for example in Romans 8:10,11 and Ephesians 2:5,6 and many, many other places.
Some conflate the last two (symbolic and spiritual) and make another supernaturalistic category in which they assert that a ritual is to be performed wherein bread becomes flesh miraculously, that is to say carbohydrate and gluten become protein by a divine and supernatural act and that the actual flesh of Christ is consumed and digested.
My own apprehension is that John 6:54 expresses that a believer in Jesus Christ partakes of the benefits of the sacrifice of Jesus Christ, partakes of his sufferings, his death, his resurrection, his ascension and his enthronement and is become part of the Body of Christ in union with Christ, by the unity of One Spirit.
And that Luke 22:19-20 is the inauguration of a symbolic act whereby believers, corporately, remember, in memoriam, the sufferings and death of the Lord Jesus, until he come.
Usually, the idea of 'parallel' passages is, particularly between the synoptic gospels, but John also, when two narratives appear to cover the same event, often from different aspects.
I would suggest that these two are not 'parallel' as they are two discourses of Jesus with differing content : one of spiritual reality and one of symbolic memorial.