That's a good question, Rolland, and I'm sure everyone who enjoys old dip and dunk photobooths has a different answer. It's also a question that, depending on your age and your geographic location, will probably be heard more and more often as digital photobooths spread around the world and take over territory from photochemical booths.
First, I'd suggest getting yourself to an old-style booth as soon as you can to see for yourself why people love them. I think a few of the things you named are among the reasons people have a special place in their hearts for these booths: first, the long strip of photos has remained virtually unchanged for more than half a century, staying power which is tough to match in the world of photography. That's not to say that a digital photobooth would be more likable if it simply printed its photos out in a strip, but the orientation is part of the magic of the photobooth.
Secondly, you say the booths themselves "look kind of antiquated," which is also definitely part of the attraction. No matter what one thinks about the look of digital photobooth photos, I don't think that anyone can really claim that the run-of-the-mill, mass-produced digital photobooths, with their half-curtains and kludgy interfaces, have any kind of charm. On the other, hand, an <a rel="nofollow" href="http://www.photobooth.net/locations/index.php?locationID=69>Auto-Photo Model 11</a> is a thing of beauty, and was even before it produced a single photo.
Personally, I prefer the old-style photobooth for two important reasons: first, the quality of the photographic image. There is simply no comparison between the razor-sharp quality of a photochemically-processed photograph and a digitally-printed one. I'm sure the quality of the digital photobooths will improve over time, but that's sort of beside the point. There's an unmistakable look produced by the chemistry of a dip and dunk photobooth, and that's the number one reason they're preferred by so many people.
My second reason is directly connected with the first: there are no previews, and no do-overs. The generation who have grown up with digital cameras, and with the ability for instant preview, deletion, and re-takes, probably don't see any charm in not knowing what the photos will turn out like until it's too late, and not being able to change the shot if it didn't come out right, but I think that restriction is integral to the charm of the photobooth. People can look totally unlike themselves, and get caught in strange, unflattering, amazing moments in a photobooth. Some of my favorite photos of my friends, family, and myself are from photobooths, where no one had any idea how they'd turn out.
I could go on with half a dozen more reason why I love photochemical photobooths, but I'll stop here. I look forward to hearing more thoughts on why people prefer dip and dunk booths, and I urge you to find your nearest booth and take some photos in it as soon as you can.