Which dating match will be more successful? Someone who is similar to you or different?

"Opposites do attract," says Dr. Neil Clark Warren, an expert of sorts in dating. "There's something fascinating about finding someone who likes you who is very different from you."

But in an interview with CNBC's "On The Money," the founder and CEO of the eHarmony online dating site warns that, over time, "opposites attract, and then they attack."

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After 35 years of counseling married couples, Warren says he's learned that "if the right person doesn't marry the right person, you've got real problems ahead. It's tough to bend people after they first get married."

Warren is a clinical psychologist and has written eight books on love and marriage. Fifteen years ago, he launched eHarmony, the site that helped pioneer the electronic dating era. The privately held company claims that 600,000 married couples have met on the site, which—if accurate—accounts for nearly 4 percent of all U.S. marriages.

The dating service business is a $2.4 billion industry, according to market research firm IBISWorld, while eHarmony has a nearly 14 percent market share among online dating sites. The leader in the category with a 21.8 percent share of the market is IAC/InterActiveCorp, which runs dating sites such as match.com, OKCupid and Tinder.

The eHarmony site charges up to $60 a month and requires users to fill out a lengthy questionnaire. Warren says: "We ask every question we can think to ask ... and we match them so carefully on 29 dimensions. We call it broad-based compatibility and it's what you have to have."

When asked what the most important characteristic is in successful relationships, Warren tells CNBC that "Intelligence is really important" when it comes to matching people for marriage.

The dating guru added that, "We have to ask the questions that get at intelligence so we can pair people up so they won't find themselves feeling hurt because the other person is saying things they don't understand."

The Internet has brought many a couple together. More than 1 in 3 couples met through an online dating site, among 19,000 couples that married between 2005 and 2012, according to a 2013 National Academy of Sciences study.

Yet an undeniable characteristic of the Internet dating age is that scores of potential partners are not out for commitment. Users that flock to eHarmony rival Tinder are notoriously uninterested in marriage—but that may be because they already are married. A recent study found about a third of the users of the fast-growing location-based app are already hitched.

"Tinder is in a different business than we are," Warren said. "Tinder is a hookup site. EHarmony takes things very seriously. We take a great interest in the fact that so many of our people get married."

Warren also says that over a 10-year period, the divorce rate of couples who met through eHarmony is 3.86 percent—far lower than a widely quoted statistic that half of all U.S. marriages end in divorce.

Within the eHarmony site are subgroups for specific ethnic or age groups. Christian, Jewish, Black, Hispanic or Asian singles have separate demographic groups, along with singles in their 30s and in their golden years.

However, same-sex singles are directed away from eHarmony to another site it owns called "Compatible Partners."

Warren called the same-sex marriage debate "the most contentious single subject in America". He told CNBC the company has tried to "weave our way through that in a careful way, and we think we've done a pretty good job."

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While the site is separate, Warren says the algorithms used by eHarmony and Compatible Partners are "similar."

Compatible Partners was launched in 2009 as part of a settlement in a New Jersey discrimination case. Warren says there is a disclaimer at the same-sex site "worked ... out with the attorney general of New Jersey.

He explains: "I didn't see a lot of same-sex people in therapy. So we don't know that area as well as we know the more conventional area." However, "We take those people very seriously and we want them to be have long-term relationships that are good."

The eHarmony founder's own marriage has lasted 56 years. He and his wife Marylyn met at Pepperdine University, married in 1959 and have been a match ever since.

"On the Money" airs on CNBC Sundays at 7:30 p.m. EDT, or check listings for airtimes in local markets.