For sure the odds are much greater in the Rugby codes. But the perception is that you don't get concussion anywhere as often or as bad in Basketball, you can play professional Basketball in almost every part of the world, and if you make the NBA you and your family are set for life.
It's not the 16 year olds, its the 10, 11, 12, 13 year olds who are just having more fun playing basketball with parents who don't have to worry about the kids health so they continue playing.
In the Rugby codes, the 10,11,12,13 year olds are having fun, but are often injured. The drop off of player numbers in the Rugby codes between 13 and 16 is a problem, but the drop off between 16-18 is over 50%. If you can't keep them in the preteen years, there is no hope in the teenage years.