Why do people bring this up countless of times, seriously.. Anyway I will do it short. YES surely senju DNA has some effect. And another thing. Notice how Kakashi bleeds? Sasuke did too, he bled a lot.. It is obvious that it depends on the amount of chakra you focus inside of the eye that depends the strength of the jutsu and thus that makes u go blind. Obviously susano takes a huuuuuge amount more chakra than any other eye jutsu. This explains why it went so fast for sasuke..
Kakashi hasn't used his eye that much. Some say, but NO he hasn't. He used the same jutsu every time, and if you compare it to how sasuke used all his MS jutsus, it will add up. Another thing is chakra control The better you control chakra the longer you can maintain the MS eye. Obito obviously has perfected his use of chakra through the eye, cause he never bleeds, and he never seems to run out of chakra. May of course also have a lot to do with senju part of his body.
Kakashi is also extremely skilled at chakra control, where sasuke is probably not, specially in the eye, since he just spammed all his ms jutsus as soon as he got it. Specially at Bee, the kages, and Danzo. Also he was healed fast after using his eye a lot, this means no rest, which in turn will cause even more damage, at least that is what we have seen countless of times with other jutsu throughout the manga. You cannot heal everything.