Rather than write many replies to those in this thread (often rehashing the same thing) I am going to reply here and address it all. There are many people claiming outdated info as current fact and misinterpreting what the differences actually imply in US v. EU occupant crash protection.
Regarding the airbags. The US now requires advanced frontal airbags in all passenger cars and light trucks. It started phasing them in back in 2003. Moreover prior in 1997 the NHTSA permitted depowered airbags which rapidly became the norm. Here is a nice FAQ with more details:
http://www.safercar.gov/Vehicle+Shoppers/Air+Bags/Advanced+F...
Now for the gist and background: In the '70s GM pioneered research into airbags (as an aside the interior of the contemporary Volvo SCC which became the 240 simply looked like a bumper car instead https://scontent.xx.fbcdn.net/hphotos-xtf1/v/t1.0-9/12042626... ). In the world as a whole (not just US) seat belt use was dismal. So initially it was hoped that they could be used without seat belts. Since the original systems were so cumbersome (for example one of them used a bottle of compressed gas) and complicated (the original acceptable switches were wighted metal balls with rings of conductors and springs) it took quite a while for them to get developed to the point that they were acceptably reliable, safe, and priced. To give an example, one consideration not immediately obvious is how the head rebounds off the airbag and into what with how much force. It took quite a lot of development that is not appreciated my most people these days, very worthwhile effort which has saved and improved the quality of life for many.
Yet by that point in time seat belt use was still abysmal in US. In some parts of Western Europe it was improving more rapidly. So policy was in US for the airbags to deploy faster and bigger (which might not be expected, but the reason is that the occupant might be not where you expect, for example sliding down into the footwell or about to be ejected from a window). The interesting aspect to this is that there is data that the US style was even better for belted adult occupants (of not small stature - more on that in a bit) in more severe accidents. This is because until the more recent advent of seat belt pretensioners and later knee bolsters it was common for occupants to slide under the steering wheel while braking or have their chest pulled in to closer than 10" from the air bag cover from same braking.
One other thing to keep in mind is that air bags were seen as a supplemental restraint system due to the lack of seat belt use in US and the requirements were initially for there to be such an SRS in place (not necessarily airbags) for certain fleet percentages by certain dates. One unexpected result was that airbag fleet saturation was lower than predicted initially due to a fluke of history. Airbags by that point used explosive charges and there were a number of snafus in their manufacture initially related to that. Ford in particular was very hard hit but a number of European makes faced shortages as well. That shortage and changing US regulation were two more reason why Peugeot pulled-out of US market since they could not surmount in a profitable manner for example. This led to the proliferation of systems that would have the shoulder belt in place at all times. Chrysler in particular benefited greatly from dumb luck in that the suppliers it had picked did not have any factories blow-up essentially and even had marketing in place at the time touting how their cars had airbags while their competitors did not.
Now back to short occupants: It was realized that the airbags were injuring or killing occupants in some cases early on. Again at that time seat belt use was still poor in US. So aftermarket airbag cut-off switches were permitted. There was also a process for having them certified for use. It was not uncommon for people that needed them (smaller drivers, those that needed to transport a child in the front, elderly, and so on) to have them installed at a dealer and shortly after that they became common place in US cars which were most likely to need them (such as pickups) as standard equipment.
