Byakugan isn't strong, in fact, it limit your abilities to "gentle fist" style. Have you ever expirienced a Hyuga performing any strong elemental jutsu? Have you ever seen them develope something great aside from their inferior fighting style?
Byakugan limits the user to be close range, it just makes a wielder believe he doesn't have any room for developement when it comes to elemental techniques, far range, and great achievements.
Sharingan doesn't limit you, moreover,it inspires and motivates you to create strong and badass techniques (Kakashi's chidori).
Byakugan is alright as Hugas seem to use it pretty well. It's a powerful defence and there is nothing wrong in being a close range fighter. Naruto is basically a close range fighter himself.
Secondly, Hugas are secondary character so we don't get to see much of them either way. Current hugas are not very ambitious, unlike the current Uchihas, so they haven't tried to creat problems and conflicts and gather power for sake of power.
Whoever tried to steal Byakugan did so to use it their advantage. Sharingan eats too much chakra and even Uchihas cannot use it for longer period without getting blind.
We never saw Uchiha's fighting with bayakugan users either. Bayakugan user can see chakra points and sense them from miles away. Sharingan has it's limits as well. Zabuza's mist had made sharingan useless.
Gentle fist may be gentle but it can be deadly. Neji had beaten the long range fighter, the spider guy carrying Orochimaru's second level seal, in Sasuke's retreaval arc despite range limits. He had to get a little creative that's it.
Most importantly do not forget that Madara, Itachi and Sasuke are exceptional fighters. Madara's sharingan isn't the only reason of his power- he is a master manipulator and a cunnig guy and Itachi ended up dead at a young age.
Sharingan itself doesn't inspire you to do anything. It's like saying that your hammer inspires you but screw driver doesn't. It depend on the individual personality.
So far, in the manga, rest of Uchiha clan memebers didn't seem very proud of their overacheiver cousins and in fact their abilties inspired only dislike and hate within clan itself. All these three EMS users only acheived alienation from friends and families and title of rouges.