An anonymous commenter wrote something worth looking deeper into:

I think this applies to all of us in the local music scene...I like the attention I get from gentlemen in between sets...usually other musicians...and I make a lot of friends that way...but the big shows with big stages (yes, I play these too)...most of the people are in awe of a woman who is not a "chick singer" and they don't know how to approach me...

It definitely is easier to meet people and make new friends at some types of concerts than at others. For maximizing opportunities for sex with groupies the dynamics are different, but I will uncharacteristically ignore sex while I write this post and just stick to the subject of forming friendships.

Playing music in public is a great way to "be somebody" and make other people interested in you. Some of those people will want to meet you, shake your hand and get to know you. Yet they do this a lot more at some kinds of concerts than others. Anonymous writes that large stages and large venues keep this from happening because they make you seem less approachable. I agree that playing in auditoriums and concert halls will generally make you fewer friends than playing clubs, but I don't think that venue size is the major part of the story. I suspect the venue's design and purpose has more to do with it than size. If it was really just about venue size, artists would make fewer new friends at exhibit openings in large galleries than in small ones. I don't think that's true, though if any artists know how it works from experience please let me know in the comments.

I think it's easier to meet people and socialize in places which are designed primarily for selling alcohol, such as pubs. Notice how it's considered unusual and almost rude for band members to pack up and go home as soon as they finish their last set - the normal expectation is that you'll at least have a drink and spend some time being social with fans and other band members. It's also perfectly normal for audience members to hang out at the venue afterwards, even for many hours if an afterparty develops. There is also plenty of opportunity to talk before the gig and during breaks. The more time everyone spends in the venue the more drinks sold and the happier the owner.

That kind of thing just doesn't happen in auditoriums, theaters and arenas whose lifeblood is ticket sales not alcohol sales. There the audience basically leaves when the show ends as there isn't much else to do. Some will stand around chatting for a little while but not for too long. Also the band will usually disappear somewhere into the back after they tear down which makes them more difficult to locate. You can still make few friends at that kind of gig, but it'll mostly be among the organizers, other bands etc. Even if you're out in the audience during someone else's set the seating arrangements facing the stage don't facilitate socializing and the amplification is more likely to render attempts at conversation pointless.

There are ways to play big stages and make plenty of friends, though. One is to plan an official or semi-official afterparty at a nearby pub. Another is to play various non-music festivals. For example, those tourism-promoting civic fests don't really revolve around alcohol sales or socializing but their purpose is to give people something to do for a few hours or even for the whole day, and that provides plenty of opportunity for people to approach the band they dug.

I guess much of the above probably also applies to making new friends when you're part of the audience, but I attend concerts where I'm not playing so rarely (once every few years) that I wouldn't really know.