We have a fallacy which just so happens to be true: Sharingan grants stronger genjutsu.
No it doesn't, not automatically.
See, Sharingan allows genjutsu to be cast through the eyes and see into the mind. The strength of genjutsu arises from chakra control (and with everything being made up of smaller bits, I'd wager that controlling certain parts of the mind/senses are easier to control than others, based on the relative strength of the caster to the castee, similar to how pushing someone back may be easier than pulling them in based on the relative strength of your leg, arm and abdominal muscles). Now the basic weakness of genjutsu, as we saw with Kurenai, is the need for handseals which gives taijutsu ages to land hits. The eye casting bypasses this weakness. Another issue is chakra control on foreign ground. Seeing into the mind (and therefore strengths and weaknesses of it) helps in directing chakra and in choosing what type of illusion to cast (if Gai is in the air, he will obviously recognise a genjutsu that sinks his feet into the ground, but would be easily distracted by a bird crapping into his eye), but the actual strength of the genjutsu still comes down to the shinobi. To say the least, the mechanics of the Sharingan do not include granting outright stronger chakra control (and therfore, genjutsu). Now we also know that concentration (and therefore time) is needed to strengthen any technique, so since Sharingan vastly shortens casting process (no handseals) it allows the caster more time to concentrate on strengthening their binding, but the actual strength is not due to the Sharingan on its own.
In a way, one could say the Sharingan grants cheats for imitating/achieving stronger control. This is why Cii considered Sasuke a genius and Danzo also complimented him. The level of control he achieved was his own work/genius, not the Sharingan. To put it another way, the Sharingan allows for dealing massive damage not through superior strength, but through critical hits.
Oh, the same applies to the Byakugan.
No it doesn't, not automatically.
See, Sharingan allows genjutsu to be cast through the eyes and see into the mind. The strength of genjutsu arises from chakra control (and with everything being made up of smaller bits, I'd wager that controlling certain parts of the mind/senses are easier to control than others, based on the relative strength of the caster to the castee, similar to how pushing someone back may be easier than pulling them in based on the relative strength of your leg, arm and abdominal muscles). Now the basic weakness of genjutsu, as we saw with Kurenai, is the need for handseals which gives taijutsu ages to land hits. The eye casting bypasses this weakness. Another issue is chakra control on foreign ground. Seeing into the mind (and therefore strengths and weaknesses of it) helps in directing chakra and in choosing what type of illusion to cast (if Gai is in the air, he will obviously recognise a genjutsu that sinks his feet into the ground, but would be easily distracted by a bird crapping into his eye), but the actual strength of the genjutsu still comes down to the shinobi. To say the least, the mechanics of the Sharingan do not include granting outright stronger chakra control (and therfore, genjutsu). Now we also know that concentration (and therefore time) is needed to strengthen any technique, so since Sharingan vastly shortens casting process (no handseals) it allows the caster more time to concentrate on strengthening their binding, but the actual strength is not due to the Sharingan on its own.
In a way, one could say the Sharingan grants cheats for imitating/achieving stronger control. This is why Cii considered Sasuke a genius and Danzo also complimented him. The level of control he achieved was his own work/genius, not the Sharingan. To put it another way, the Sharingan allows for dealing massive damage not through superior strength, but through critical hits.
Oh, the same applies to the Byakugan.