I got Brave New World during the recent Steam sale and just finished my first game, playing as Morocco as they seemed well-placed to try the new trade routes and culture system. Thought I'd post my impressions.
I really like the way this was implemented, which surprises me as when I first saw that it was unit-based I feared it would similar to Civ2's basic implementation. I had imagined an abstract system like espionage would be better. But the fact that trade routes can be lost so easily, which is effectively wasted production, encouraged me to build up a navy earlier in the game than I typically would in order to defend from pirates. The way that trade routes also transmit religion, science, and culture makes them a subtly powerful mechanic.
I liked the UN stuff in Civs 3 and 4, but it always came so late in the game that it barely had any impact. It's good that they put it earlier in the game this time to fix that, and this is probably the best implementation they had for such a mechanic so far. As someone that normally only half-engages with city-states, this gave me a new reason to focus on them and get more alliances.
I love this idea of offensive and defensive culture. I aimed for a culture victory, and nearly won with 6 of 8 civilizations under my influence and 2 more above 80% when time ran out, so I won a score victory instead. I might actually have won a culture victory had I known about the tourism bonuses for arranging types of great work in specific buildings, I guess I'll know better next time. But it was fun to attack the other civs with something other than my armies and watching as they slowly fell further under my influence.
This was probably my favourite part of the game. I've always been a little disappointed in the geopolitical aspect of the Civ games, so I really liked the way that ideologies forced me to rethink old relationships. I chose Freedom as that seemed well-suited for a cultural victory, which put me in the same faction as Siam, Venice, and Babylon. The Ottomans, who had original picked Order, quickly rebelled due to cultural pressure from Siam and myself, joining the Freedom fold. All five civs, who used to be at odds with one another to a certain extent, suddenly found ourselves in a very stable pact of mutual friendship.
Mongolia, the Celts, and Assyria were Autocratic states, while the Mayans managed to resist cultural pressure to remain the sole Order nation. When Mongolia conquered several city-states, I denounced them, which led to the Celts and Assyria denouncing me. But as my cultural pressure on Mongolia grew, rebels began to attack their capital (which I could see due to my spy in the city). A Mongolian city eventually flipped to my civilization, and a few turns later Mongolia revolted and adopted Freedom. This angered the Celts, who soon turned on Mongolia and invaded.
This is the sort of stuff I always wanted in Civilization, and it's finally here. I've only played one game so I'm not able to tell if they've balanced all these mechanics right, but I'm really pleased with what I've seen so far.