I'm not suggesting that adults will always learn faster than children. You will no doubt notice that you did not spend your time the same way that your children did. Did you spend 24 hours a day thinking and struggling in that foreign language? There is a big difference to being exposed to language and concentrating on it. Restricting your self to thinking only the thoughts that your language enables you to think is difficult for an adult (well, impossible really).
I'm not entirely unaware of the literature in the area. I spent 5 years of my life teaching English as a foreign language. A large percentage of that time was spent doing research in language acquisition. As far as I am aware, ever since Chomsky the general consensus has been that there is no different mechanism for language acquisition in children than in adults. There are still some researchers who disagree, but that happens in every field and is healthy.
But, you aren't going to beat a child in learning a language unless you do some very specific things. That's because they spend 24 hours a day, 7 days a week learning language. Even when they get to school, their school work is primarily surrounding language activities until they get to be about 10 or so.
An adult's secret weapon is the ability to read. If you use that to direct your learning, then you can go quite quickly. Like I said, though, getting to an adult level of proficiency in less than 10 years is pretty difficult, but it's not impossible by any stretch of the imagination. The same level proficiency for a 10 year old child is very, very unusual.
For things like accent and getting tones correct all the time, that's a bit of a different story. Only about 2% of adult learners achieve native level proficiency in that kind of thing. But it's not something that will hold you back from normal communication. Event then, I'm aware of some specific language training you can do to help, but most people are not really interested in going that far.