That link you gave is for turbulence, not a prepared emergency landing. Remember, there are different dynamics for take-off and landing than there are for turbulence.
It depends on the airline. I read that the child was held to the floor landing on the Hudson but that shows you how inconsistent the press can be (experience speaking, especially with aviation!) My first airline just had the baby in the lap but the second had the babies on the floor (only prepared, there is probably no time in an unprepared emergency landing). The floor helps hold the child in place, our instuctors explained. The parent only has to hold them in one direction.
Again, flying is so safe that there are no reliable statistics on this. There are many preparations for emergency landings that turn out fine (remember that if you are ever in one!) The pilots will order one for some small mechanical problem (that has a small potential of being dangerous) and you'll get to see the whole routine. I never had to do one in 13 years of flying but many of my domestic coworkers did. Please note that domestic is not less safe. I simply did fewer take-off's and landing's doing long-haul international than they did.
But there is a lot of difference between airlines. I had to relearn the commands, the positions, etc. There is a difference even with how they want the adults to brace themselves. There is virtually no information on which way is best just because there aren't enough incidents to make a reliable comparison. They can't say "In accident X, the brace position was too..." It just doesn't happen!
Btw, the fly vs. drive argument is debated. Some say that the airlines pressure the FAA to not bring in a seat-for-each passenger policy for commercial reasons (i.e. to sell more seats). I certainly can't drive from Europe to California so trips like ours' shouldn't be counted...
I'll go ask one of my coworkers if the second airline still does this but I can only find out for them, not the other companies.