To boil it down for you:
Tohno Shiki sees lines and dots.
Ryougi Shiki sees lines and dots.
Tohno Shiki can kill anything that's a physical object. He could also kill Akiha's jail hair, but this was retconned as being a Jougan ability and not actually Mystic Eyes.
Ryougi Shiki can kill anything. We know she can kill people, physical objects, magecraft, diseases, ghosts, and intentions.
If Tohno Shiki strains himself, he could also kill poisons, vampire blood, and even Arcueid's link to the world. Doing this strains and possibly fries his brain.
Tohno Shiki needs Mystic Eye Killer glasses because he is not suited to the Eyes and his eyes will overload his brain and kill him.
Ryougi Shiki doesn't need glasses because her body is perfectly suited to the Mystic Eyes.Misconceptions:About the concrete box:Touko tells Araya Souren that if he really wanted to trap Shiki, he should've used a concrete box instead of magecraft barriers.The misconception:
People usually interpret this as "Her Mystic Eyes are weak against concrete, but not magecraft." From that, they conclude "Tohno Shiki has stronger Mystic Eyes than Ryougi Shiki for killing physical objects, but Ryougi Shiki can kill anything non-physical with ease."The truth:
Shiki is disarmed at this point. Neither Nanaya nor Ryougi can kill a concrete box without some kind of cutting implement, but Ryougi Shiki can
kill the magecraft barriers with her bare hands. That was Araya's mistake. At no point in Rakkyo was it suggested that Ryougi Shiki has difficulty killing physical objects.Ryougi Shiki cannot see dots:The misconception:
I think it was sheer inattentiveness, this one, or maybe just basing it off of the OVAs - not sure how they handled it. Anyway, people seem to believe that Shiki cannot see death dots.The truth:
Shiki dot-stabbed Fujyou Kirie (ghost girl), Asagami Fujino's appendicitis, and Araya Souren in the first fight at the apartments. (Araya Souren has all sorts of ungodly protections against mystic eyes of death perception, so he still had a considerable lifespan left after the dot-stab, hence the second fight.) If you need a quote, here's one from Chapter 1 of the novel, against Fujyou Kirie: "One on each of her legs, one on her back, and one point on her left chest. The cutting section called death can be certainly seen. The one on her chest would be a good one to aim for. That would be an instant kill." So, Shiki can definitely see dots.
PS: The Type-Moon wiki has an article on it: http://typemoon.wikia.com/wiki/Mystic_E ... Perception
It's kind of messy to read and might actually confuse you more, though.