I will try to make it brief. As far as I see it, from playing both ICW 2.1 and the 2.2 demo, the difference between the Captain and Admiral difficulty level is mostly in the way how aggressive the AI is. In my experience, the AI is much more aggressive on Admiral, and attacks you as often as it can. However, by throwing all of its fleets at you it doesn't really defend properly, and by the end of a GC it becomes very easy to capture the remaining AI planets as there would be little to no fleets defending them. On Captain, the AI doesn't attack as often, but keeps a much more defensive approach, and even though it would be easy throughout most of the GC, it gets interesting by the end, when the AI stacks huge fleets on its final few planets. For instance, I was playing the Empires at War GC as the PA on Captain, and the IR had 3 planets left, but each planet had fleets of +250, with the closest one consisting of 2 Executors, 17 ISDs (both 1 and 2), and 34 Victories (same). Plus a whole bunch of Lancers, Strike Cruisers, Immobilizers, etc. So in some cases, playing on Captain can be even more challenging towards the end, because it guarantees you several very tough battles. While on Admiral it gets very easy after a certain point, even if it's tough at the start. As Maldrood in the demo it's really only challenging a little bit until you build your first Bellator, and it becomes a one way fight from there.
Am I right, and that's where the difference between Captain and Admiral lies, or does it depend on GCs? I never had RaW installed, btw (I heard it influences the AI).