The NHTSA and IIHS tests are complementary. They both simulate somewhat different types of crashes, all of which are among the most common and deadly in real life.
IMO, if a vehicle has crash test ratings that are all IIHS "Good", NHTSA "4-star" or higher, it's very safe. If you also have stability control and side curtain airbags, you and your family will be very well protected.
As a side note, the NHTSA does correlate each of its star ratings to an increased risk of injury in real world crashes. From their website:
Frontal star ratings indicate the chance of a serious head and chest injury to the driver and right front seat passenger. A serious injury is one requiring immediate hospitalization and may be life threatening.
= 10% or less chance of serious injury
= 11% to 20% chance of serious injury
= 21% to 35% chance of serious injury
= 36% to 45% chance of serious injury
= 46% or greater chance of serious injury
As with the frontal crash ratings, a serious injury is one requiring immediate hospitalization and may be life threatening.
= 5% or less chance of serious injury
= 6% to 10% chance of serious injury
= 11% to 20% chance of serious injury
= 21% to 25% chance of serious injury
= 26% or greater chance of serious injury
The IIHS lumps some categories together when they do the correlation for frontal offset crashes to real world fatalities. "Best Pick" and "Good" are grouped together, as are "Acceptable" and "Marginal". So, in reality, the differences between those categories is based only on differences in the crash testing and not a correlation to real world data. This may be important or trivial, it's impossible to say.
If you want to see how safe your vehicle is overall, try checking
http://www.informedforlife.org/CRSriskorder2006.pdf . This website combines NHTSA crash tests, IIHS crash tests, rollover risk, weight and safety features into one rating comparable across all vehicles. The way they combine all this data is not arbitrary, it's based on published statistics and studies. The 2006 Passat does quite well overall with a score of 75, much better than average.
Almost every model on the first two pages is a great choice for safety, particularly if it can be equipped with side curtain airbags and stability control. The only few exceptions are those with many missing entries, such as the Saab 9-3, Lincoln Navigator, Dodge Durango, etc. Those might also be very safe, but there's not yet enough data to say for sure.