Personal experience and personal drive are very important factors in learning how to swim, as well as learning anything else, yet the biggest factor is learning capability for kids learning how to swim on their own or in swim lessons.
Some kids learn slower than others, that's just how it is. Some people will go through life either figuring everything out for themselves or getting everything the first time.

Other people will get some stuff at first and not other things, and others will have to try extremely hard to figure out what they need to know. Your learning capability will determine whether or not you will learn many things. A kid could get so frustrated because he can't do a certain swim stroke that he will give up and never learn to swim. Learning capabilities need to be noticed before anyone is taught anything so that way the instructor knows how to teach kids to swim with swim lessons.

All of these factors affect how fast a kid learns to swim. While these factors collide and interfere with each other most of the time, every now and then they work in perfect harmony. Now, while Jimmy and Susie were in swim lessons, Tommy was at his home pool teaching himself how to swim. With a little help from dad, Tommy, in two weeks has learned to successfully swim front crawl and the back stroke (monkey-t-pull), he has learned to hold his breath under water for seven seconds and swim under water, and he can float on his back.

Susie, who takes lessons every Saturday for a month and practices everyday after school with her mom, can swim front crawl and back stroke, hold her breath for about five seconds, and float on her back for a second or two; after a month long period. And finally, Jimmy, who takes kids swimming lessons every day after school, learns to swim front crawl, can hold his breath for nine seconds with his goggles on, and can swim under water to pick up diving rings at the bottom of the three foot, with his goggles on. Once again, that is after a two week long period.

As you can see, these three kids, for the most part, are probably at or around the same level of knowing how to swim, although they all learned a different way, and in a different period of time. So I guess the answer to the question, "which is faster," is neither, yet both at the same time. While taking swim lessons is a more reliable way for your kid to learn how to swim, it is not always faster than some other kid teaching himself. What I've been trying to show you is that every kid, or person, learns at a different rate. Even still, personal experience, personal drive, environment, and a persons learning capabilities will also differ from person to person, making each person unique in what they learn, how they learn, and eventually how they will teach what they know.

As for what I think, you should enroll your kids (and you if you don't know how to swim) in a swim class as soon as they are of age, or as soon as you have time. The faster you get them into the routine of swimming every so often and into a class where they will learn the proper way to swim, the easier it will be for them to progress through the Learn to Swim Program.

Even if you don't belong to a pool or have your own right now, you never know when you might actually be that one out of a billion that wins the lottery. Of course then the question is - pool or jacuzzi?

References:
American Red Cross Swimming and Water Safety Book
American Red Cross Fundamentals of Instructor Training Participants Manual