I think the ying chakra sealed away by the death god is the "spiritual" part of Kyuubi's chakra. Remember in the beginning of the series its mentioned that chakra is split into two sides, spiritual and physical, and to get stronger you have to train your body for physical and meditate (not sure) for spiritual. Right now Naruto only has the physical part (yang) which might explain why he takes on the physical attributes of Kyuubi the more he uses it. If this is correct then I wonder what the effects of unsealing the other part of Kyuubi's chakra would have on Naruto's mind.