Jesus taught that through him comes our purification (i.e. righteousness), and it is as a result of this righteousness that we obtain eternal life.
Paul taught that through a mysterious union between the believer and Jesus Christ—wherein the believer would be counted righteous—the believer would be raised from death while non-believers would remain in their sins and therefore not enjoy eternal life.
For 3 examples from Paul's letters:
This is relevant because Jesus commissioned Paul, which is unlikely if Paul would just go on to just misrepresent a core part of Jesus's message. More than likely, given the weight of what he experienced and how he dedicated his life to it, Paul went on to represent Jesus and the Gospel with extreme care and accuracy.
Mt 3:11-12 — [John the Baptist said] The axe is already laid at the root of the trees; therefore every tree that does not bear good fruit is cut down and thrown into the fire. As for me, I baptize you with water for repentance, but He who is coming after me is mightier than I, and I am not fit to remove His sandals; He will baptize you with the Holy Spirit and fire. His winnowing fork is in His hand, and He will thoroughly clear His threshing floor; and He will gather His wheat into the barn, but He will burn up the chaff with unquenchable fire.” (cf. Jn 1:29 — the Lamb of God who takes away the sin of the world!)
This is relevant because Jesus accepted baptism by John the Baptist, which fits best with the hypothesis that John represented and understood Jesus (and his message) rightly.