Alright let me explain the answer you seek in detail with some help from the manga here is a breif description of the sharingan
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Generally speaking the sharingan has the capability to percieve, predict, and copy all ninjutsu. It has the ability to break any Genjutsu, and it can forsee most taijustu but if its too fast...
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That will happen...(poor sasuke)
Now to your MS problem
First the basics
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So in order to awaken the MS you have to kill your cloesest friend we know this...in order to awaken EMS you need to have your siblings eyes '
Every Uchiha has different eyes and variations of power
For Kakashi's MS...
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For Itachi's MS...
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For Sasuke's MS...
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Now for the different variations of EMS
For Sasuke's EMS...
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And for Madara's EMS...
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So now that you have seen the differences in the MS and EMS and the various versions of each type you can come to the conclusion that each type of member in the Uchiha clan would have different eyes but not only that to some up your question about the amateratsu and tskyuomi.
Those are the powers of sasuke's family and that branch of the uchiha. Think of it this way hinata's byukagan is more sharper then neji's becasue she is of the higher family. Neji's is more skiled at using his during battle while Hinata is a tracker.
If your still with me just keep reading it will click.
Now we don't know how the uchiha family is for branches but we can understand that if sasuke were too hve a son to awaken MS they would have Amaterasu or Tskyuomi as their bloodline ability. If Madara were too have a son (Hope not) They would have his powers.
I hope all this and the general answer...answers your question.