Previously, he was Executer & Supreme Commander, but now that Darth Disney has bought the Franchise, his position within the Empire is unclear. So I was wondering, what is his RANK now within the Empire? Is it the same, or something different?
Vader never had a rank -- he was outside the chain of command. Ranks and grades belong to set hierarchies. Lord Vader held the offices you described in the old EU. I think it's likely he'll end up with a similar position in the NEU: after all, the Supreme Commander term came from an action figure which was trying to capture his role in the Empire. There's little reason that will change. There were some changes within the EU itself though: formerly Lord Vader was subject to the whims of the grand vizier, but the Rise of Darth Vader changed that. There are already indications the NEU will follow. Missa ab iPhona mea est.
Why would his rank change? It's safe to assume being a Sith elevates him above the vast majority of the imperials, unless the situation calls for him to observe and assist like on the Death Star. Anyone challenging Vader and his authority that isn't on the Emperor's do not kill list is pretty much screwed.
Yeah, that's probably the best answer. Technically supreme military commander, second only to the Emperor, etc., might be more detailed, but basically anyone who talks back is either Force choked or killed by lightsaber, so with that, his rank is slightly irrelevant. The Death Star meeting is probably the perfect example of this. Sent from my iPad using Tapatalk