>Ryougi's eyes are actual Mystic Eyes of Death Perception that she can turn on and off at will. Tohno's are actually Jougan which is what he inherited from the Nanaya clan, but since he kinda died, his mind became oriented to death so he sees death manifested as lines, and he can't turrn it off.
>Ryougi's eyes will see lines on anything that needs some level of energy (be it life or otherwise; connection to Akasha) to sustain itself, hence she can see barriers that normally aren't visible, and in the case of Fujino, her powers. She can't see lines on innanimate objects such as walls, chairs, etc...as these things don't need some sort of external source of energy to manifest.
>Tohno sees the existance of the object, hence why he can see lins on innanimate objects. His natural born Jougan (truth-seeing) eyes might let him see barriers and invisible things of that nature, but he was never trained to use them so those abilities are lost. Whereas Ryougi's ability is not the result of stupid mistakes colliding with eachother to create her Mysitc Eyes, Tohno's is, so his mind goes under incredible strain to maintain this connection with Death for him to see the lines. This is also why when he tries really hard, he can see the dots which represent the death of the existance of the thing. This connection with Death is also what will probably kill him.
>Tohno Shiki can see the lines of barriers and the such if he knows what to look for, but unless he's told, he might as well be affected like any normal person. This is how he was able to kill off the poison in Kohaku's blood in Hisui's story, almost going blind in the process, and kill off Sacchin's vampire blood from "infecting" him (Sacchin, isn't it sad...?).
>It's really a matter of opinion as to who's is more powerful, both have their uses in certain situations.