Babylon
Babylon remains a great choice for more defensive players. You encounter more barbarians in this expansion, so make sure to get your Bowmen on hills as spotters to protect your trade units.
Denmark
The Vikings delight in raiding Cargo Ships in any map with a heavy amount of water. In a map where crossing the water is the only way to get to a City-State or to another nation’s city, their ability to quickly embark and pillage comes in handy.
Inca
If you start in a section of the map with plenty of hills or can settle and hold a hilly area, you’ll have the advantage of keeping your precious Caravans safe as they travel over hills with impunity.
Korea
The path of Science has changed little, so Korea is largely unaffected by Brave New World. You’ll need to trade with other nations and engage in Diplomacy, but unless you need the money, stick to trading with City-States so that the other civilizations can’t benefit from your frequent lead in Technology.
Mongolia
Diplomacy? Trade? Late-game victory conditions? The Khan cares not for these things! As an early- and mid-game rusher, Mongolia is more likely to use Trade Routes internally for Food and then Production, and they're hoping to win each game long before the many late-game changes start to influence anyone.
Polynesia
Polynesia is a good contender for a civilization focused on late-game Cultural or Diplomatic Victory. Their Moai Heads give them extra Culture, and their focus on exploration over the sea means that they’ll be able to start working on befriending all the coastal City-States as soon as they find them. Of course, like all civilizations with a focus towards a specific type of terrain, a Polynesian player will do best if they play on maps that cater to their powers. Archipelago maps make life much better for these islanders.
Spain
Spain really needs to focus on exploration as early as possible if they hope to get the most out of their bonus for discovering and exploiting Natural Wonders. They’re a solid mid-game civilization, so find the Wonders early. Use your military to keep them safe and settle a new city there or take them away from another civilization if they’ve settled there already. Over time, the Culture and Gold benefit contributes toward a Cultural Victory, but don’t expect it to be quick!