Let’s start with the basis of the question and define some terms. The earliest documents we have for the life and teachings of Jesus, apart from a few scattered references in Paul, are the first three Gospels. The majority of scholarly opinion dates Mark to somewhere between 60 and 80 CE (with post-70 being most common lately), Matthew to the 80s, and Luke to somewhere in the 90s or 100s. John, because it uses titles and imagery for Jesus that are borrowed from the emperor Domitian (esp. “my lord and my God” at 20:28), is almost always dated to the mid-90s or later. Already we see a challenge for historical Jesus research--the earliest (surviving) accounts of his life don’t appear until at least thirty and probably more like forty years after his likely death. Going by dates alone, John isn’t on much worse footing than Luke.

The Synoptic Problem complicates this. I won’t go into a whole description--I’m sure Wikipedia does fine. But the gist is that Mark, Matthew, and Luke share a whole bunch of material, sometimes verbatim, AND Matthew and Luke share a whole bunch of material that Mark doesn’t share. There’s almost no textual overlap with John. What’s the relationship between these three texts? The most popular solutions posit the existence of an earlier document, called Q (short for the German word quelle, or “source”). The theory in most of its forms goes that both Matthew and Luke used Mark and Q to construct their Gospels, and that Mark did not know Q, and that Matthew and Luke did not know each other (basic diagram here). Q is dated to anywhere from the 30s to the 60s, but is often assumed to contain a lot of oral tradition dating to the time of Jesus. Because the three Synoptic Gospels supposedly preserve this older source, agree on so much, and are relatively down-to-earth compared to John’s very highly philosophical and even mystic bent, historical Jesus research usually prioritizes them over John.

Now to the question. Does John contain any historical information that the Synoptics don’t? How would we know? If a story appears only in John--say, the wedding at Cana in chapter 2--we have no basis to confirm or deny any kernel of historicity. There’s no separate “list of weddings that Jesus attended” that does or does not mention Cana. A normal way that historians of antiquity approach this sort of thing is with a kind of guarded acceptance. If Suetonius says that Augustus did something and no other text confirms it, we generally accept at least that Suetonius is faithfully representing his sources. Unless there’s a solid reason to argue that the thing didn’t happen, we’ll include it in the historical record, maybe with an “according to Suetonius” attached to it. So, did the wedding at Cana happen? None of the Synoptic Gospels claim to be exhaustive of Jesus’s activities, so there’s no reason to say “It’s not in Matthew therefore it’s not real,” or similar. And surely some weddings happened at Cana. Maybe Jesus went to one, and the subsequent oral tradition or the author of John elaborated.

So why might we argue that the wedding didn’t happen? The main reason, absent more solid proof, would be if it fits too well with some kind of agenda that the author of John is setting up. Multiple scholars have shown that John portrays Jesus with heavy reference to Dionysus (Dennis MacDonald immediately comes to mind, but there are others), and, in fact, some Dionysus temples had festivals at which jars of water locked in the sanctuary overnight miraculously turned to wine by morning. So some people might say that the Cana story lines up too well with the Dionysian theme, and therefore can’t be considered historical. Of course, a counterargument might say that historians would consider the miracle an addition, anyway, with or without the Dionysian connection, so there’s still no reason why the wedding itself can’t have been historical.

That’s the basic method. It’s really asking whether things are plausible, rather than 100% provable. If you had some way to prove that zero weddings happened in Cana between the years of 0 and 150 CE, that would affect the plausibility of the scenario, but we don’t have that. The Synoptics are usually given more weight in historical Jesus work because of their agreements and because Mark and Matthew are earlier than John, and so is Luke if you’re accounting for Q, but plausibility is still the basic criterium for them, too.

Now here’s where things get weird. There are some theories of the Gospel of John that suggest it was written in multiple stages. John 15 and 16 interrupt the action in an awkward way--at the end of chapter 14 Jesus finishes his sermon and says, “Let’s go,” and then stands there and talks for two more chapters. Some people argue that those two chapters are a later addition, which implies that, possibly, there was a version of John written before the 90s that got added onto to create the text we have today. Then there’s the issue of the Beloved Disciple. Tradition and most scholarship identify this disciple as John. Verse 21:24 claims that the Beloved Disciple was a direct source of the text, and possibly an author of an early version, which would make at least parts of John eyewitness accounts of Jesus, or close to. This doesn’t necessarily mess with dating. If he was young during Jesus’s life--say, in his teens or 20s--he could have lived into the the end of the first century (and 21:20-23 might imply that he lived a long life and recently died). There are also theories that the author of 1 John was the (or an) author of the Gospel, and 1 John 1:1 seems to claim that its author was an eyewitness of Jesus. That would, potentially, make John a much more important text for understanding the historical Jesus. I’m not sure how prominent these lines of thought are in historical Jesus research, but they get tossed around in Johannine research.