The idea behind HDR photos is that they look more similar to what our eyes see than regular photos. In many cases this leads to particularly bright and vibrant photos, but in the case of the iPhone 4 and iOS 4.1's HDR feature it didn't always seem that way.
While we've only played around with the feature for a while, we noticed that it seems to favor—or even privilege—highlights. This makes some of the HDR photos seem washed out next to their non-HDR counterparts while making the colors look more natural. It also means that the iPhone 4's tricky white balance troubles are practically an issue of the past.
It's worth nothing however, that the HDR feature does seem to struggle a bit in case of environments with low level lighting or situations where there isn't a dynamic range to exploit. My bathroom appears to cause one of those situations because my poor rubber duckies confused the HDR feature and resulted in a funky, messed up image despite the iPhone being held perfectly still during the photo:
That little quirk aside, the HDR feature seems to lead to far more natural looking photos in general. But since it's not always easy to predict when this will be the case, I recommend toggling the photo settings to save both the HDR version of a photo as well as the normally exposed version.