The paralles between their two heroes are easy to see, including being martyred by the establishment. So one might understand that a group of followers continued after the death of each of their teacher-leaders. That John did have disciples already during Jesus' lifetime is testified in the NT Gospels, for example when John's disciples come to Jesus to ask him if He really is the Messiah, or "should we look for another?"
The Gospel of John (Evangelist) is obviously supporting the Jesus-is-Messiah conviction. This first chapter wants to "help" the John-is-Messiah folks see that right from the start John himself never claimed to be the Messiah, but always and only said the other guy was THE ONE. But why is that important?
That list of revealers includes the "big" guy from the O.T., Moses. So v. 17 makes it "perfectly clear," that although Moses was a God-revealer and indeed something special, he doesn't measure up to Jesus. All of chapter 6 in John's Gospel is basically a comparison between Jesus and Moses and the "bread" that God offered through each of them. Moses is finally not in Jesus's league. God used Moses to "give his people bread from heaven (=Sinai)," but they all still died. Not so with the bread that Jesus gives, that Jesus is. So there is a quantum leap of difference between Jesus' portfolio andthat of Moses. "Grace and Truth," whatever that all will mean as the story unfolds came via Jesus and only via Jesus.
D-2
Worse than that (says this text) is that if you just merge Jesus in with other revealers, you miss out on the unique stuff that comes only with him. In John chapter one it's called "light." The opening 4 verses of the whole chapter indicate what's the big deal about Jesus. This "light," namely, is the very "life" that comes from God. So to be light-less is to be life-less. Here the diagnosis is getting heavy. But it's even worse than that.
D-3
Not to have the life from God that Jesus brings = not being God's own kids (see v. 12 & 13). And if you really are not God's kid, but keep thinking you are, you are in deep trouble. Especially if you once were God's kid-in-Christ, and now have forfeited it, then you're disinherited from all that your previous "god's-kids" connection gave you. Which has eternal consequences--and they start now already.
P-2 (Good News to cope with D-2 above)
Believing this Jesus for what he REALLY is (i.e., not a generic Jesus) is the key to getting (back) to be God's kid. The Greek word often translated in v. 12 as "power" is really a legal term. It's more like 'rights" or "authority". So the meaning is: To all who received Jesus (for what he really is), who believed on (entrusted themselves to) his name, he gave the "right," the "authority," to call themselves God's own kids-with all the perks that come along with such "rights." Now isn't that something! If we are God's kids, then we're on a par with Jesus himself, God's child number 1.
Therefore "Believing Jesus" = having God's own life. Getting the same paternity, genetic coding that Jesus himself has. See 20:31 for corroboration that "believing [Jesus] = having the life [God's own] that is in his name."
P-1 (Good News to fix up D-1)
Believing means "having" God's life. Living that life means witnessing, witnessing just as John did. Helping the priority-confused worldlings around you get their priorities straight. Pointing to the real Messiah in your words and deeds. That means, of course, having your own priorities straight--both about Jesus, and (as a result of that straightened-out priority) about everything else in your life. If, for example, as you do so, someone concludes that YOU are this person's Messiah, then the Baptist gives you your lines right in this Sunday's text. V. 29 summarizes John's (and our) public witnessing.