I bought Civ4 about a week ago. I had played Civ3 a decent amount so I started on Warlord and was so handily winning that I stopped playing. So I decided to jump up to Prince and am slightly shocked that I'm going to win this one as well. I am playing on an island map which might distort things some, but Russia and I were the other civs to share an island so I had to deal with her (thankfully I founded cities that helped cut off her settle choices) and because of her cultural ocean blockade and my tech choices, I didn't start trading with other civs until significantly later than usual. So, despite those problems, after I overcame Russia, I'm definitely the real power. I only wish naval warfare was more pronounced. Next game I'm going to be German or England on a land map and I might just bump it up to Monarch... haven't decided yet.
Overall, I'm surprised I've done so well because I remember the "even" difficulty on Civ3 (Monarch, I think it was) could give me fits at times. I really liked most of the changes to this version of the game (I thought I'd hate not having seperate strength/defense numbers but it's actually worked out well).