That's because Palpatine wasn't the Sith Empire. He was a single individual. He didn't have an entire culture inexplicably change. Even the centuries after him, the reborn Empire still feels aesthetically more similar to the Galactic Empire than the Republic. There's no reason the Sith would just abandon everything that made them unique just to be more like their most hated enemy.
I believe Palpatine's quote was believed to be a reference to the New Sith Wars. I suppose it doesn't really matter, though. The very existence of the Sith Empire in TOR is a pretty big, pretty recent retcon and it's resemblance to The Galactic Empire this far back in the timeline makes no sense. The writers could literally have anything happen and that's what the canon would be. There would be little need to justify it.