In theory, the SI should be more about plotting and secretly working your way to the top, much like Palpatine. That's who the class was originally modeled after.
However, in practice, the SW's story does it much, much better. Nearly every enemy or rival you come across (Jedi or Sith), you are given the option to corrupt them, turn them to the Dark Side, or convince them to serve you. So right out of the gate you have more options for building your power base. The SI in general seems just like a psychopath (while not a problem in itself) when he kills people, rather than someone who actually takes into account the tactical soundness of his decisions.
The entire SW Act I by itself features more manipulation than the entirety of the SI's story.
which is something the SI never really gets to do.
The SI isn't even able to manipulate his own companion,
into turning to the Dark Side. So much for a master of the dark arts!
The SW's manipulations are supported partly later on by
however it is clear that the plans are coming from you. Even before
the SW very clearly had a plot in place
The SI however, seems like he is stumbling around, taking people's suggestions, and somehow haphazardly ending up in a position of greater power, for example
and yet still fails to achieve many of his own objectives by the end.
And at the end of both storylines,
I attribute this mostly to the fact that the SW has much higher quality storywriting and voice acting than the SI rather than anything to do with the overall concept of the class. The SW really felt like an intelligent, honorable, yet cold and ruthless manipulator, but who could still pack a very hard punch in combat. I practically had my own army of fallen Jedi whom I had corrupted and a few Sith Lord lackeys to boot.
There are also more roleplaying options for the SW. At nearly every critical story moment, there are 4 or 5 branching paths rather than just 2 for the SI. While the SI could usually only have the option to either kill the person or let them live, the SW would usually be able to choose between "honorable death", "merciful death", "keep them and torture them for more information", "convert them to your side", or even "witty sarcasm/snarkiness" (especially towards Darth Baras). Playing a LS SW was truly as convincing as playing a DS SW and the voice acting reflected it. A LS SI seemed somewhat out of place, as you'd have sudden, schizophrenic sounding lines like "It's YOUR turn to die now!" even if everything you said beforehand sounded perfectly reasonable. Bravo to the SW voice actor.
Overall, I just really loved the moments when the SW could tell his Jedi adversaries that he sensed fear and anger in them. My favorite lines to say were something like "I sense your darkness, you have already fallen. Release your anger", and "Strike me down, Jedi!" as it had the very iconic feeling as when said by Darth Vader or Darth Sidious in the movies. As far as I recall the SI never got to say anything nearly as cool.