Not really.
A LS Imperial can be just as honorable as a LS Republic character. A DS Republic character is a bad apple in a "good" system (though, it's debatable just how good the Republic truly is..). An LS Imperial is someone who is trying to do the right thing while protecting the Empire's interests. It's a challenge, but actually feels quite satisfying believing you can make the Empire a better place than it is. Ofc, the situations where you do turn out to be more noble and honorable than your Republic counterparts are incredibly satisfying.
LS Imperials still have to massacre slaves (Dromund Kaas), murder the political rivals of their questgivers (basically all over the place), destroy democratic insurgencies against Imperial rule (Balmorra, Corellia), slaughter noncombatant colonists (Taris), commit blatant war crimes (several planets, especially Taris), and, y'know,
fight for a government that is worse than the Nazis.
You have the option, as an LS Imp, to behave 'honorably' in
some quests, usually ones associated with class storylines or planet arcs, and sometimes that behavior is juxtaposed with Republic NPCs who are doing the sorts of awful things that Imperials do as a matter of course. It would be embarrassingly obvious to point out that those are exceptions, not the rule. I mean, isn't it just a
little preposterous for a Sith Warrior to march into an Organa military base, kill most of the soldiers there, then tell General Gesselle Organa that oh, you're not really interested in fighting, you just wanna stalk this girl she used to be friends with years ago, please tell me where her parents are kthx? That's the sort of thing that passes for 'honorable' actions for Imps, and it's silly.
At the end of the day, fighting for the Empire means
fighting for the Empire, and for the perpetuation of one of the most disgustingly unethical, immoral, violent, destructive, fratricidal governments in the history of the galaxy. Pretending you can separate an LS Imp from that context is the worst sort of self-delusion: it's the same crap that leads Lost Causers to argue that the Confederacy wasn't fighting for slavery, or that old
Wehrmacht veterans used to claim that the army wasn't complicit in Hitler's atrocities and in the Holocaust.
An LS Imp player can try to mitigate this through the course of her class storyline: an LS Agent can promise to work as a double-agent for the SIS, an LS Grand Champion can go rogue and assassinate Darth Tormen, an LS Warrior can form a little anti-Sith cabal with Jaesa, and an LS Inquisitor can avowedly use her position on the Dark Council to push 'reforms', whatever the hell those are. If those storylines had any actual impact on the game, that might shift the debate somewhat: an LS Imp wouldn't be 'better' than a Pub, but you could plausibly claim that they were atoning for past sins or something. But when you head over to Makeb, Oricon, and the rest, your LS Imp is right back to being an obedient pawn of the Dark Council's flavor-of-the-week Sith Lord. The moral decisions that seem redemptive after Corellia become meaningless.
You mention fighting to make the Empire a better place. How exactly is that supposed to happen? You'd have to destroy the Sith, because the Sith are intrinsically evil and perpetuate the worst sort of atrocities on the people of the galaxy. Without the Sith, then, what's the point of the Empire? The entire government is designed around servicing the whim of the Sith in general and the Emperor and Dark Council specifically. Take the Sith away and the Empire is left with no reason to exist whatsoever.
When I wrote a fanfic about an LS Sith Warrior, I simply could not reconcile all of the stuff that an Imperial character does with any basic sense of morality at all. Headcanon ended up having to take priority over a faithful recreation of the game's plotlines. Even though I tried to give the characters the best of possible motivations, and even though I tried to create a faction of Republic enemies even more cartoonishly evil than Revan appears during the Foundry plotline, I still couldn't make it work in my head. Two hundred pages of writing and hundreds of hours of gameplay down the drain.
Of course, there are very logical reasons for this problem. Continuing to develop the class stories would come at a fantastic cost in time and money, and it would be unfair to expect BW Austin to follow through on that. Yet at the same time they need to continue the storyline and release endgame content, because otherwise they wouldn't keep a lot of the players that they have. So they continue the faction questlines, but the constraints of writing mean that they have to paint Pubs as good little Pubs (which they mostly did anyway) and Imps as good little Imps.