very good answers already
I'll put another word for some things already stated:
- the AIs still start with warriors. It's your last chance (incas excepted) for warrior rush. Why not do yourself the treat?
- the huts now pop barbs from time to time. Nothing to be really scared of, but don't pop the hut next to your capital with your warrior. Let the capital's culture get it.
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6k Man said:
The hardest thing for me to let go of was that I would not necessarily be atop the scoreboard all the time.
Don't be afraid, that's just the way it works, no problem, but it's a bit odd when you're not used to it.
Now for some "new" items.
IMHO, prince is the first level where the AIs can actually win. It still requires huge amounts of land, but it happens (I mean space or culture, a dumb diplo win is possible at all levels) So prince is also the first level where you may want to go worker stealing.
Tech trading starts getting a bit interesting, because the AIs actually have something to trade. It may sometimes make sense to lightbulb and trade widely, depending on the game (loads of war = low tech AIs, as you certainly know).
On noble you can live with terrible diplomatic relations. On prince, they can outproduce you sometimes and you don't want to be the center of a dogpile. Don't switch to the religion you founded if other have a different one.
Other than that, I'm sure you'll be fine.