Ok let me tell you all my opinion as to why i believe perfect susanoo is kakashi's not obito's.
As you cam tell kakashi's PS basically looks just like sasuke's, aside from the scar. In the chapter they mentioned kakashi being the famous copy ninja twice which asother people guessed he merely copied sasuke's PS as right befor kakashi came sasuke had his PS activated. Also many MS usually have unique abilities. Sasuke can control amaterasu(shape manipulation,turn it off) shisui(koto) itachi(i would have to say his control over tsukiyomi). For obito you may say it is kamui. When he awakened the MS that was the ability he got. I believe it is because he activated that he got kamui. Madara said that it was as if the rock went through when he was supposed to be crushed it must be linked to that. Kakashi however has always used the sharingan to copy jutsu. This leads me to believe that the MS reacted to this which gives him his own unique ability while using MS he can copy more powerful jutsu such as PS and make is his own. An ability unique tto him while he has both MS