It is not comparable with the Didache as it servers a different purpose
In c14 of the Didache "On the Lord's day meet and break bread and offer the Eucharist, after having first confessed your offences, so that your sacrifice may be pure." Interesting is the action is referred as a sacrifice.
The best estimate of the date of the Traditio Apostolica is AD235, and there is only fragmentary documents that survive in the original Greek.
Prior to this we get a glimpse of what the Eucharistic celebration looked like from Justin who wrote his first apology around 150.
"After we have baptized him who professes our belief and associates with us, we lead him into the assembly of those called the Brethren, and we there say prayers in common for ourselves, for the newly baptized, and for all theirs all over the world...After finishing the prayers, we greet each other with a kiss. Then bread and a cup of water and of mixed wine are brought to the one presiding over the brethren. He takes it, gives praise and glory to the Father of all in the name of the Son and the Holy Ghost, and gives thanks at length for the gifts that we were worthy to receive from Him. When he has finished the prayers and thanksgiving, the whole crowd standing by cries out in agreement; "Amen." "Amen" is the Hebrew word and means "So may it be". After the presiding official has said thanks and the people have joined in, the deacons, as they are styled by us, distribute as food for all those present, the bread and the wind-and-water mixed, over which the thanks had been offered, and also set some apart for those not present. (Justin first apology, c65)
It is true that Hippolytus' writings are later, (217) they give a clarity to otherwise shadowy outlines of the shape of Christian worship prior to the 3rd cent. It represents the earliest we possess of laws or ordinances regulating the clergy, liturgical functions, the order of rites to be observed especially conversion and baptism. The similarity to the Eucharistic prayers offered today is striking.