The grounded realities, once again, is the One Sith highly study the knowledge and even culture of prior sith orders and empires, and are trained by Krayt for the purpose of controlling the galaxy and facing the Jedi in direct combat.
Sidious likes to keep his people under-trained, aside from the formal apprentice. The Brotherhood of Darkness didn't have access to the knowledge of many sith orders. The One Sith have neither of these problems, it has access to great force knowledge and uses it because it wants it's people strong enough to do the job.
Heck, shall I also point out that the One Sith pioneered force-based technology, something that's barely been touched on since the Ratakans?
The cultures of the TOR Sith and Legacy are somewhat different, but they do both value strength as a way to advancement, and actually are more similar to each other than a number of other orders. Both have an Emperor who's desires ultimate overrule all other factions, unlike the Old Sith Empire and New Sith Wars, where there were numerous sith lords aside from the top who had a great say in things. Beneath this emperor, there were powerful Sith who would conduct things in said emperor's absence and handle much day to day stuff. Beneath them, there'd be both other powerful lords and commanders who try and advance through success, and lesser sith beneath them who try to gain such ranks. In those matters, they are not too different. It's more acceptable in TOR to kill your boss or rival... but even then, it's limited by the higher ups so as to not disrupt things, and internal rivals for power do exist in the One Sith as well.
Notably, the One Sith also *don't* have the policy of people being ranked highly purely on politics. There's no Vowrawn equivalent, because skill at internal politics would be of little use to Krayt/the order as a whole.
So politically/internal structure, the One Sith, again, value strength, much like the TOR Empire does, even if they do have some differences.