As a student of the prestigious Ouran High and a member of the Host Club, it's obvious that Kaoru and his twin, Hikaru, enjoy a very luxurious life. Although on the outside they appear to be the same, Kaoru tends to be more reserved and inwardly emotional than his brother, as well as calmer and more level-headed. What similarities in personality they do share usually show through in different ways; to quote the series, 'Hikaru's actions are one level meaner than Kaoru's'. This doesn't mean Kaoru doesn't have the same intentions, he's just more subtle about it. More than a little mischievous, they both enjoy playing jokes on other people, usually doing so out of boredom or to get an amusing reaction.
The twins are rarely seen apart, and although he doesn't let it show very often, Kaoru relies heavily on his brother. This is far from a one-sided thing; Hikaru's reaction to separation would just be a bit more obvious. While Kaoru would become somewhat nervous, Hikaru would be twice as such.