I've been visiting the central Texas area and recently helped my brother out at the Austin Gun Show. (He's stationed here in the Army, not a local hipster.)
The gun show seems to be the only other major themed convention these days aside from the sci-fi / video game convention. (Not counting corporate-audience conventions, but only pop culture ones.) I went to two nerd conventions in the '90s when they were just getting started, but I have a pretty good idea of what the newer ones are like too, both from osmosis and from poking around just now to find out how much tickets and tables cost (both way more expensive for the fan con).
We can learn a lot about the state of our culture by contrasting the two types of gatherings, mostly reflecting a populist vs. elitist orientation.
Celebrity worship. At the gun show, there were no panels of speakers, autograph booths, "have your picture taken with So-and-So" booths, and so on, that cater to fan-boys. Those are common at sci-fi / video game conventions, which are attended more by fans and followers than by hobbyists and participants.
Infrequency. A given nerd convention is usually only held once a year, while a given gun show may meet up four times a year. Looking at all the different locations where they're held, this gives the attendants of a fan convention only a handful to attend, usually crammed together, like rare vacations. It's the one or two times per year that they're willing to leave their home, join a crowd, and pretend to be social. With all the locations for gun shows, each meeting several times a year, there's one every month that you could go to. It's a more regular meet-up, like church or college football. All else equal, greater frequency of interaction bonds the attendees closer together -- more in the abstract, feeling like they belong to the community of "people who go to gun shows," and not necessarily recognizing individuals from previous shows.
Spectacle / Intensity. This somewhat includes the topic of celeb obsession, and the related topic of dressing up in costumes, which you don't see at gun shows but are common at fan cons. The booths at nerd conventions have a lot more bling and wow-factor thingies going on, rooms full of arcade video games to play for free, karaoke, live music, parties, and so on. Since fan cons are less frequent, they must make up for that by being more intense, in order to glue the members together. Still, they appear to meet too infrequently for the greater intensity to produce the same effect as the gun show phenomenon.
Social awkwardness. While fans may not be openly hostile toward each other at nerd conventions, they certainly are awkward and uneasy interacting with each other, giving lie to the idea that they're stepping out of themselves and taking part in a Mardi Gras kind of atmosphere. * By contrast, at the gun show folks show much more camaraderie toward one another, and not only for fear of disrespecting a man with good aim. There's more openness, joke-telling, and good cheer in general. So, the product of frequency times intensity per event must be greater for the gun show than the fan con.
Demographic insularity. Nerd conventions, whether based on pop culture or the greater Nerd Way of Life (atheist conventions, etc.), constantly wring their hands about their sub-sub-sub-culture being too male, too young(ish), too white, too suburban, too middle-class, too a-religious or anti-religious, and too-whatever-else. At the gun show, you see a more representative mix of races (like Spanish-speaking Amerindians with cowboy hats), guys and girls (generally being dragged along by their boyfriend or husband, but showing a good attitude about it), and elementary school-aged children up through the grandfatherly age groups, city-slickers and suburbanites and middle-of-nowhere-livers. My impression is that females felt less creeped out by their fellow male attendees at the gun show, compared to their greater state of alertness at a fan con. Probably from both sides, the females being more anti-social and paranoid there, and the males being more desperate and awkward.
Most noticeably of all is the range in social class -- you see never-married, burn-out / drop-out types who haven't been to church since the 3rd grade, and whose philosophy (and praxis) of the good life is fast cars and loose women, right alongside the God-fearing nuclear family who stay out of trouble and are net wealth-producers for society. One smokes, sports tattoos, and shows up in Black Sabbath t-shirts, while the other abstains, maintains neat personal hygiene, and wears khaki shorts or pants with a polo shirt. Unlike the typical nerd at a fan con, though, both tend to keep their hair into adulthood, and are less obese than the American average.
There are probably other differences to cover, but those are the main ones that stick out. Feel free to ask in the comments about something major you think I didn't cover.
As a final historical note, it's worth pointing out that the gun show is more a product of the rising-crime / outgoing era of the 1960s through the 1980s. "Gun show" first regularly appears in the New York Times during the early '60s, and the original bigass gun show, the Fort Worth Gun Show, began in the early '70s. They have continued strong into the '90s and 21st century, probably with some major changes reflecting the falling trust and rising paranoia of the times, but still recognizably from a more populist and outgoing era like the '60s, '70s, and '80s.
The major Comic-Cons, however, are a product of the past 20 years. There were comic book conventions before then, but they were like the gun shows, only for comic books. My dad sold comic books as a side venture in the early '90s during an industry bubble, and I helped him out at many conventions. They never had speakers, panels, autographs, etc., and nobody dressed up in costumes, held a nerd-themed party, etc. It was just a bunch of tables staffed by comic book vendors, with comic book readers (and speculators) milling around to look for rare finds and good deals. The fan pilgrimage is a product of the cocooning Millennial era.
* No carnivalesque event is as hierarchical and celebrity-worshiping as a fan con -- at Mardi Gras, nobody is following anybody else, or otherwise mindful of leaders and idols. It's closer to decentralized mob rule.