Well, going off what I get from leaving Battle Info on on my chat window, most of the attacks appear to be physical damage. But, I did get hit a few times for chakra damage from mobs. And de-equipping some of my chakra resist gear did appear to increase damage taken from them.
This wasn't exactly a thorough test, mind (+ I wasn't doing this on a DE and I don't have a resist chip). So, take from that what you will, I guess.