Are modern day missionaries the equivalent of what the Apostle Paul was at one time?
The twelve apostles and other apostles mentioned in the New Testament, like Paul, where a special type of apostle for the first century only. These apostles had the ability and authority to write Scripture for the New Testament.
They also formed and founded new works, such as churches in new cities and any other type of Christian organization. For instance, they formed the Deacon ministry in Acts 6 so they could continue to minister as apostles but have people to serve in certain functions in the church that required attention, such as passing out food rations for widows.
The Canon of Scripture is closed. With the finishing of the book of Revelation by the apostle John in 95/96 AD, no Scripture can be written. What we have as the 27 books of the New Testament along with the 39 books of the Old Testament stands as the Christian canon.
For this reason, the apostles of today, modern day missionaries, cannot write Scripture as the first century apostles did. They had the authority to write Scripture because they walked with Jesus or personally knew him.
Paul is the only one people may contest as personally seeing Jesus. Yet the Scriptures clearly say that he saw the risen Jesus just as the other apostles did in the upper room and other places on the road to Damascus (Acts 9).
Because they personally knew Jesus or walked with him throughout his earthly ministry, they understood and could reiterate his teachings to the Church. He opened their minds to receive the understanding of how to interpret the Scriptures already written (Luke 24:45).
So for modern day apostles, what we call missionaries today, they still fulfill the role of an apostle. They form and found new works all across the globe. When they found churches, orphanages, Christian organizations, parachurch ministries, and all these types of new works, they are fulfilling the function of the apostle.
As they preach the gospel all around the world in different languages, they are fulfilling the function of the apostle. Like Paul and the churches he founded, they act as spiritual fathers and mothers to these organizations they found.
So the only difference between a first century apostle and a modern apostle, a missionary, is that modern day apostles do not write Scripture. Everything they do and say must agree with Scripture.