I don't think the Empire wishes to bring order and stability to the galaxy. At least not the upper tier rankings of it, and as the Empire will kill their own command structures for failures, some will kill just because they were looked at wrong or because you're not Human/Sith. And even those who may think something is wrong within the Empire, tend to change their tune when they're given power.
Republic however has their own problems and just because the Republic as a whole is generally good, doesn't mean they all are.
To sum it up:
The Empire = Absolute power corrupts absolutely.
The Republic = With great power comes great responsibility.
Empire itself is a stability and order, so whenever it grip reaches, subjects become part of order. Killing for failures is essential to get rid of weak and useless material that may cause even bigger havoc if spared. Sith does not kill for the wrong look, unless it is in public, and someone openly disrespect them, manifestation of power is required. Those who think that something is wrong are usually less intelligent people with weak characters that want to be equal with others just for the sake of it, typical and dangerous.
Absolute power rarely leads to corruption, but such statements are well known for people who try to remain within heart of corruption in democratic states of Republic. It is ill propaganda manufactured to liking of simple folk who feel entitled to rule their countries whenether they cant count to 10 or are simply idiots ( rarely individual agrees to his intelectual limitations ).
Republic is based on corruption, semi mob rule where senate live on bribes. Republic is negation of advancement for the sake of unnatural ideals.
only the most intelligent, powerful and with proper personality people deserve to rule ( about 1% of whole population ) - and that is The Sith Empire, place where everybody seeks challenge, advancement and further development.
The Sith Empire
, place that you want to die for ( and most probably you will )