Alright, as seen by Sasuke during the fight of the hokage during the 5 Kage summit, Sasuke used Amaratsu. He also used his left eye to create the flames, but just the flames, not able to move them with his left eye. He used his right eye when the Raikage was about to KO him(1) to cover his Susano'o to block his attack and force the Raikage to sever his arm. (2)
Now we know that Obito can use Kumai to teleport (?) to a different dimension, and it was claimed by Madara that one Sharingan is not as powerful as a Uchiha with both eyes intact. I think that, perhaps, Obitos remaining Sharingan can use Kumai, but only to a limited extent, and Kakashis Sharingan can do different things with Kumai since he has the left eye. Just as seen with Sasuke making the Amaratsu flames appear with one, and changing their form and making them move with the other.
What do you think?
TL;DR: Each Sharingan has different special techniques. However, each eye does certain things within that technique.
It's weird, watch Sasuke vs Killer bee: He creates flames and puts them out all with the same eye. And putting out the flames is considered manipulating. Itachi was able to manipulate the flames when he fought with Sasuke, White Zetsu even stated that it was Itachi that put them out himself.
Different conclusions are reached when one fact is viewed from two separate points of view. When that happens, there is no immediate way to judge which point of view is the correct one. There is no way to conclude one’s own conclusion is the correct one.
Re: Power of the Sharingan.
Itachi is kinda the exception and Madara is unknown