all the things in 1 Corinthians 15:1-4 are written in John's gospel. they are part of the "these were written" that is in John 20:31
both are informing us that Christ is God -- that is John's primary purpose throughout his book. both John and Paul are relating what Jesus Himself said in John 11:25-26. this is the faith that saves, from the beginning to the end, to the Jew and also the Gentile.
if you have 1 Corinthians 15:1-4 but you do not believe Christ is the Son of God, that He is I AM manifest in the flesh, so what that a mere man, even a good man, died in your place? does that save you? so John, who wrote this some time after the synoptic gospels were written, concentrates on demonstrating the deity of Christ - and records that He died for our sins and was resurrected in order that we might have life, that by believing on Him we will be saved.
this is not a 'different gospel'
John 20:31 = 1 Cor 15:1-4 = John 11:25-26 = 2 Peter 1:3-4 = Proverbs 30:4