Ok to clear things up.
Byakugan can see chakra a lot better then Sharingan, flow/tenketsu is what the Byakugan can see, Sharigan can only see the flow.
However the Sharingan can slow down perceptive time, allowing the user to predict movements, and the Byakugan has a 360 degree view naturally.
The difference of the eyes themselves is that;
Sharingan/Byakugan can see chakra flow.
Byakugan can see Tenketsu.
Sharingan can "slow down" time.
Byakugan has a 360 degree view.
Since the Byakugan has ONE more ability then the Sharingan it makes it a superior eye, WITHOUT Dojutsu.
Now if you include Dojutsu, the Byakugan is screwed the second Tsukuyomi is cast, as the 360 degree view cannot let you focus on ONE specific thing. You eyes see 360 degree's, aside from the Thoracic Vertebre, in which a Byakugan user would have to use the SMALL area of that to block the ability to see into the Mangekyo Sharingan users' eyes, in order to do this the Byakugan user would have to be facing backwards; this is neither realistic nor relieable, and thus the Byakugan user would instantly get put under Tsukuyomi.
Now this is where things get a bit more complected, as earlier on in the series we learn that Genjutsu effect the brain only, where as in the Kakashi gaiden Rin's body chakra was screwed up as well; along with that Tsukuyomi is an advanced Dogenjutsu, and we don't exactly know 100% how it works.
If it worked with only the brain the Byakugan user would be able to see the chakra flow in his/her brain being abnormal and instantly break out of it, WHILST still being able to view the opponent, 360 degree view. Since that is the Sharingans way of battling Genjutsu, I would assume the same theory would be accurate for "Superior"
eyes.