I do not intend to solve the debate here. For those who are interested in this topic please see the book Five Views on Apologetics.
When I say "Jesus and the Apostles were Evidentialists" I am using the term evidentialist (or evidentialism) in a much broader sense to mean "presenting evidence or appealing to facts in order to demonstrate the truthfulness of the Christian faith." Apologists from various methodologies (including the classical, evidentialist, and cumulative case approaches) can agree on the biblical nature and effectiveness of this broader definition.
Reading through the New Testament it is hard to deny the fact that both Jesus and the apostles backed up their claims by appeals to facts and evidence. In other words, they were evidentialists.
As you read the verses below pay particular attention to how often reference is made to the resurrection of Christ, especially in the book of Acts. This really shouldn't be surprising. After all, it was Jesus Himself who said,
An evil and adulterous generation craves for a sign; and yet no sign will be given to it but the sign of Jonah the prophet; for just as JONAH WAS THREE DAYS AND THREE NIGHTS IN THE BELLY OF THE SEA MONSTER, so will the Son of Man be three days and three nights in the heart of the earth (Matt. 12:39-40).
In other words, the Resurrection is the sign given to mankind as evidence for the truthfulness of the Christian faith.
"But so that you may know that the Son of Man has authority on earth to forgive sins" - He said to the paralytic, "I say to you, get up, pick up your pallet and go home." And he got up and immediately picked up the pallet and went out in the sight of everyone, so that they were all amazed and were glorifying God, saying, "We have never seen anything like this."
Inasmuch as many have undertaken to compile an account of the things accomplished among us, just as they were handed down to us by those who from the beginning were eyewitnesses and servants of the word, it seemed fitting for me as well, having investigated everything carefully from the beginning, to write it out for you in consecutive order, most excellent Theophilus; so that you may know the exact truth about the things you have been taught.
When the men came to Him, they said, "John the Baptist has sent us to You, to ask, 'Are You the Expected One, or do we look for someone else?'" At that very time He cured many people of diseases and afflictions and evil spirits; and He gave sight to many who were blind. And He answered and said to them, "Go and report to John what you have seen and heard: the BLIND RECEIVE SIGHT, the lame walk, the lepers are cleansed, and the deaf hear, the dead are raised up, the POOR HAVE THE GOSPEL PREACHED TO THEM.
The He said to Thomas, "Reach here with your finger, and see My hands; and reach here your hand and put it into My side; and do not be unbelieving, but believing." Thomas answered and said to Him, "My Lord and my God!"
Therefore many other signs Jesus also performed in the presence of the disciples, which are not written in this book; but these have been written so that you may believe that Jesus is the Christ, the Son of God; and that believing you may have life in His name.
The first account I composed, Theophilus, about all that Jesus began to do and teach, until the day when He was taken up to heaven, after He had by the Holy Spirit given orders to the apostles whom He had chosen. To these He also presented Himself alive after His suffering, by many convincing proofs, appearing to them over a period of forty days and speaking of the things concerning the kingdom of God.
Therefore it is necessary that of the men who have accompanied us all the time that the Lord Jesus went in and out among us - beginning with the baptism of John until the day that He was taken up from us - one of these must become a witness with us of His resurrection.
Acts 2:22, 24, 32
"Men of Israel, listen to these words: Jesus the Nazarene, a man attested to you by God with miracles and wonders and signs which God performed through Him in your midst, just as you yourselves know... God raised Him up again, putting an end to the agony of death, since it was impossible for Him to be held in its power... This Jesus God raised up again, to which we are all witnesses..."
Acts 10:39-41, 43a
We are witnesses of all the things He did both in the land of the Jews and in Jerusalem. They also put Him to death by hanging Him on a cross. God raised Him up on the third day and granted that He become visible... to us who ate and drank with Him after He arose from the dead... Of Him all the prophets bear witness...
Acts 13:30-31, 34a, 37
But God raised Him from the dead; and for many days He appeared to those who came up with Him from Galilee to Jerusalem, the very ones who are now His witnesses to the people... As for the fact that He raised Him up from the dead... but He whom God raised did not undergo decay.
And according to Paul's custom, he went to them, and for three Sabbaths reasoned with them from the Scriptures, explaining and giving evidence that the Christ had to suffer and rise again from the dead, and saying, "This Jesus whom I am proclaiming to you is the Christ."
Therefore having overlooked the times of ignorance, God is now declaring to men that all people everywhere should repent, because He has fixed a day in which He will judge the world in righteousness through a Man whom He has appointed, having furnished proof to all men by raising Him from the dead.
"...other than for this one statement which I shouted out while standing among them, 'For the resurrection of the dead I am on trial before you today.'"
"So, having obtained help from God, I stand to this day testifying both to small and great, stating nothing but what the Prophets and Moses said was going to take place; that the Christ was to suffer, and that by reason of His resurrection from the dead He would be the first to proclaim light both to the Jewish people and to the Gentiles."
...who was declared the Son of God with power by the resurrection from the dead, according to the Spirit of holiness, Jesus Christ our Lord...
1 Corinthians 15:3-8
For I delivered to you as of first importance what I also received, that Christ died for our sins according to the Scriptures, and that He was buried, and that He was raised on the third day according to the Scriptures, and that He appeared to Cephas, then to the twelve. After that He appeared to more than five hundred brethren at one time, most of whom remain until now, but some have fallen asleep; then He appeared to James, then to all the apostles; and last of all, as to one untimely born, He appeared to me also.
1 John 1:1-2
What was from the beginning, what we have heard, what we have seen with our eyes, what we have looked at and touched with our hands, concerning the Word of Life - and the life was manifested, and we have seen and testify and proclaim to you the eternal life, which was with the Father and was manifested to us.