There are some datacrons like the +Cunning datacron on Tatooine that are in major towns. For example, there is a Republic datacron in Anchorhead and a matching Imperial datacron in Mos Ila.
Is it possible to fight your way through the opposing side's town, and obtain their version of the datacron in addition to the one on your own side?
You do not get a double bonus by claiming the other faction's datacron. I confirmed this on Corellia by hopping onto the railway and running all the way to the Imperial landing area and then locating the datacron in that part of the planet.
It gave me the same dialog as though I had clicked on a Republic datacron that I already had; basically "You have already learned the power from this datacron" or something of that sort. Others may say that you are denied access.
Bonus fun fact: The tiny vista that you ride through on the Republic train just before reaching the second adventure area on Corellia is almost identical to the new Black Hole quest area. A couple of the buildings or props have been moved, but the layout is identical. Because of the angle you see it from the train, you can hardly tell.
Datacrons are tracked as quests. As such, they are only available to one faction.
Since Patch 4.0, Datacrons are now Legacy-wide. While you still cannot initially acquire an opposite-faction's Datacron, any that you do acquire are instantly made available to all of your characters regardless of faction. The Legacy & Achievements window (press Y) now has a section to track which Datacrons you've unlocked.
