I have, it seems I'm the only one in this forum without problems. First impressions are good, the Tactical battles are just as incredible as they were in EIC but with up to 15 ships per side rather than the old 5, while in Strategic mode the game is about twice as fast which is compensated by the new 0.5x speed so everybody can be happy. The gameplay itself feels a bit unusual but nice, kind of Settlers done with ships rather than people, if that makes any sense people on Paradox forums are comparing it to Port Royale and the Patrician series, neither of which I've tried so I can't speak from experience.
Overall though, it's a very fun game, and things like the randomized ports, production chains and larger battles should make it much more replayable than EIC was, I believe. Still, there's a lot yet for me to try, I had just gotten my third colony and my first production chain when I stopped playing, but the game feels very promising.
Two omissions I could see, however, are Anti-Aliasing and a Multiplayer mode, the former perhaps due to my ATI card though EIC supports it just fine, the latter a somewhat sad absence though considering EIC's servers were a barren wasteland it's not a huge loss either. Ohh, and I miss the old suave voice of EIC's campaign, CotA's voice acting isn't bad, but it's just not the same
Aaaand that's that, there's a demo on the official website for those that don't know what the game is about, though *that* one I tried to download many times without success, so YMMV.