BNW changed the feel of the game significantly. Trade caravans/boats, rebalanced gold, Piety available at start and new factions make it play out very differently from G&K.
War has been changed completely. AI players are no longer psychotic in the way they fight. Previously, I find the game ended in two scenarios - everyone likes me, or everyone is sieging me. AI players engage in good diplomacy amongst themselves, and you have to do so as well.
Don't try to befriend everyone - pick your allies, and maintain that friendship. When declaring war, make sure you present it properly to the world - that is, don't break a Declaration of Friendship with war, and DO denounce beforehand. There's a reason the AI players do so. Bring a friend or five with you.
AI will not declare war at you randomly. They will prepare, try to gather allies, and will not always feel confident enough to attack you. This may be patched somewhat in the future, but war is no longer a guarantee. They WILL work to screw you over, though, from spies to missionaries to planting cities in front of your settler. Arguably, the AI also knows how to bait YOU into attacking it.
Massive spread of empires has been nerfed ---- and personally, I'm happy about it. You can't plop cities willy-nilly, and you can't go conquering every city you find. Cities impose a fairly severe 5% tech cost penalty - which is fine, if you can bring the city size up quickly and build as many science buildings as possible. But you need to balance it out, not expand too quickly, and overall be very aware of territorial limitations.
When it comes to late game, I seem to have a slightly different perspective on that. Late game is ALL about victory conditions. And while you are pursuing yours, so is everyone else. So instead of hitting ENTER watching the build time go down by a turn, you should be using money and/or military and/or religion to sabotage ANYONE who could threaten you.
In other words, you are ALWAYS at war. Economically, politically, culturally and scientifically. Amongst many other aspects.
BNW brings different mechanics, some hotly argued right here in the forum. However, it invites a broader range of gameplay decisions and I think that is fantastic. My only criticism is that with war political penalties, and tourism, the game shifted a lot of early-to-middle-game focus to victory conditions and I don't like that. I rarely play a game to completion. But then again, if I don't, it doesn't matter as much