I just looked at A. T. Robertson’s (he was a great Baptist Greek scholar) comments on John 3:16, and he states that these are not the words of Jesus, but rather of John. In the NET Bible, the quotation marks end at John 3:15, indicating that these translators agree. Other translations leave the quotation marks until the end of chapter 3. In the final analysis, it does not matter, because “all Scripture is inspired …and profitable” (2 Timothy 3:16). Red letter Bibles inform us that it is Jesus who is speaking, but whether Jesus is speaking in the Bible or not, the message does not change. The apostles, like John, simply speak for our Lord (Hebrews 2:3-4; see also 1 Corinthians 14:37).
The Bible Knowledge Commentary states, “Whether this verse was spoken by John or Jesus, it is God’s Word and is an important summary of the gospel.”
I must simply say that I am not certain. If it were really important, then God would have seen to it that it was plainly stated as the words of our Savior. Since the interpretation and application of this verse will not change either way, I just don’t agonize about it.