I have't been able to tell the actual difference between both. My guess is that, Kakashi's MS tech can be used from afar while Obito needs to be in contact with you first. I may be wrong but feel free to correct me.
P.S. I'd also like to know if they are both called Kamui. I remember the first time Obito revealed his MS, he said something like "the true power of kamui" The question here is, if they were seperated for a while, how did they both know it was called kamui?