My brainstorming session is over. For what I've gathered, the answer is Owarji's answer.
--The Uchiha clan was revered for their powerful manifestations of ninjutsu, but this was primarily Fire-based ninjutsu.
--The Uchiha clan was most famous for their Kekkei Genkai, the Sharingan, but only select members of the clan actually progressed to obtain it. Further, very few shinobi have obtained the further evolution of the sharingan-- madara, izuna, shisui, sasuke, itachi, and (I wanna say) Setsuna to make it an even 6. Out of these 6, only two received EMS, Madara and Sasuke.
-- The Senju clan was revered for their mastery of many ninjutsu. This is as Owarji has explained, "the clan of 1000 hands". The Uchiha clan may have had their powerful fire techniques, but these techniques can easily be doused by water. This may be pushing it too far, but it's not a far stone throw to suggest that the Senju clan got its nickname because many members were able to do more than 2 elements' worth of ninjutsu. 3? 4? 5?
It can be concluded, then, that the Uchiha clan got the raw end of the deal. Their members had to be exceptional to actually manifest what their clan was famous for as it's been suggested that select few members were actually pushed to that limit.