The difference is, you're not supposed to meet people at the movies or the theater. Today's dance clubs, with their overpowering volumes, are still theoretically social venues. Compare this to the 18th Century social dance - also music-oriented, also social, frequented by people of the same age groups. The most important similarity is that both dance venues are particularly interesting to single people who want to meet other people - yet with no conversation, you can't learn anything about your partner(s) except stamina and body type.
That is rather the point, of course. Toleration and encouragement of promiscuity lead to a different style of dance. Rock, hip-hop, and techno invite us to judge dancers on the body they were born into and/or how often they work out. Add in freaking, and dancers can be judged on their willingness to act out specific, unmetaphorical sex acts in public. To "hip" (sex-crazed) young people, completely uninterested in starting either platonic friendships or stable families, old-fashioned balls seem laughably stodgy and prudish.
Of course, they were anything but. Anyone doubting this should watch a decent Jane Austen adaptation. (I'm thinking in particular of the BBC's Pride and Prejudice, with Colin Firth and the unforgettable Jennifer Ehle.) Wit flowed freely; a distaste for boring conversation is surely as old as speech itself. What I think might be easy to overlook is how important the structure of the dances was. A couple could converse, but would never be completely out of earshot. Tawdry or profane conversation would bring a swift reaction from any number of scandalized gentry, but with sufficient subtlety, almost any idea could be put across to one's partner, because the couple would not be in hearing distance of any single person for long.
In other words, the ball was an explicitly social gathering in which young women would be completely secure against the advances of rakish young men, yet also have the opportunity to evaluate their prospective husbands on several extremely important criteria. By observing a young man's adherence to the dance steps, she could evaluate if he had the ability and inclination to follow rules. By listening to him converse, she could tell if he was an absolutist about rules and propriety (i.e., a complete bore), or if he was willing to liven things up by cleverly tweaking the nose of authority from time to time - a moderately brave act with several sets of parents, maiden aunts, dowagers, and grouchy grandfathers watching.
A man who could dance a long time showed that he had stamina. A man with strong hands and a brutish habit of shoving his partner would be as disfavored as a man with no strength. A budding alcoholic who reeked of drink and staggered across the floor would mortify his partner - better to dance with someone who drank in moderation.
Naturally, young man would be evaluating his prospective wives as well. We are continuously told that men are shallow, evaluating women as if they were various cuts of meat. Yet at our 18th Century social dance, evaluating a woman on her looks alone was an obvious recipe for unhappiness. Premarital sex carried the risk of social stigma and, in some periods, death on the sword of angry father or brother. Moreover, divorce was generally unacceptable, so marrying a shrew was basically a life sentence of marital strife. These facts were clear to young people of all but the lowest social classes.
The important thing, though, is that a meat-market gaze would tell you very little about the women at an 18th Century dance. A woman's face would be visible, and her upper chest in some fashions, but the laundry list of details harped on by contemporary women's magazines would be largely invisible. Toned abs! Pish posh. Cellulite! What's that? The twin fears that drive so many of our young women to despondence - that a young man will value her for sex and nothing more, or conversely, that young men will sum up her flaws and find her "not hot enough" - were completely absent from the 18th Century dance.
A girl's chances of marriage would ride partly on the prettiness of her face. This is the sort of superficial yet intractable feature which makes life seem so heartbreakingly unfair to teenagers. In every other way, though, the 18th Century dance seems tremendously fair. A morbidly obese woman would be harshly judged, but in a way that is fair because obese women have trouble carrying pregnancies to term. A man was respected, not considered "egotistical", for wanting children, and his desire for a wife that could bear children was honored. Similarly, it would be hard to disguise a disfiguring disease of the sort that would render a woman barren or a man unfit to provide for his children. Minor blemishes, on the other hand, would be gracefully hidden by the dim candlelight.
Anyone who set their mind to it could learn enough grace and manners to be a passable dance partner and guest. It is inconceivable that someone be excluded from one of these gatherings because of being a "dork" or not being "cool". What could not be faked, at least not for an extended period, was wit, charm, and attentiveness - the raw materials of compatibility, and eventually love.