Gaffer Tape said:

And, finally, as for Tarkin and Vader, that's simply explained. In the context of the first movie, the Sith were a warrior tribe who allied themselves with the Empire. The Empire itself was not ruled by a Sith. The Emperor was a politician, and Vader, a Sith, was working for the Empire. The Empire obviously respected (to a certain degree) the powers of the Sith, but, again, Vader was considered a "dragon." The true Empire was built on military strength, not the force. Obviously that gets a bit more difficult to swallow when the Emperor is retconned to be a Sith.

Good points, but you could only know any of that if you read the Annotated Screenplays.

In the context of what's actually on the screen, I always assumed a much simpler explanation.

In Star Wars, Tarkin was the boss, Vader was some kind of an enforcer, apparently specifically tasked with getting the rebellion. After Tarkin went boom, Vader got promoted (hence his awesome new ship and no one to tell him to stop with all the choking).