Some gear you can only use if you have certain dark/light levels. Though these are only visual differances, and there should always be equally balanced option regardless of what you choose.
What it does for your story in the long run I cannot tell until I've played through the entire class story, but your choices in quest dialogs often changes the outcome of the quest.
D= How?! He is awesome! He exists to remind you that you are supposed to be a ******. So stop sparing innocent and defenseless people.
The only reason people hate him is because they are ***** idiots who want to get a female companion.
Saber Strike deals x damage spread over 3 strikes, for a total of x/3 per strike.
Trash strikes twice, dealing y damage, for a total of 2y damage, y damage per strike.
Trash is better than Saber Strike.
There are probably more gear like that to obtain through the levels. Some you may even get from quests or vendors. I think they know there are many who want cloaks. As torhead gets more updated with screenshots we will probably find many.
I did BT around 5 times and I saw different gear dropping each time. As for heroics on Korriban, did all of those as well, didn't see it drop but it might be.