At Prince you can out-expand, out-tech, out-produce and out-power the AIs simultaneously, but you may as well adapt strategies now that will serve you well as you advance beyond Prince.
It's funny you say this. I'm playing a game at Prince right now because I wanted to work on my peaceful REXing technique, and I am finding this to be both very true and hard to accomplish at the same time.
Specifically, I am on a continent with Suleiman, Roosevelt, and Mansa Musa. From the very start, I've had to be at Monarch level of efficiency to keep up with the first two on Power and the last has been a gigantic pain in the assa assa with technology. When the first three religions got founded on other continents, I saw an opportunity and grabbed the one from CoL and ended up being the owner of the holy city of the one true religion on our continent, which was key for the peaceful REX. No religious strife.
Now, the other continent is HIDEOUSLY backwards, just as I would expect when I play prince, but on my side of the world, we're looking at rifles and cannons (and in my case Cavalry sometime around 1500, which is pretty damn early for a Prince game.
If freekin' Mansa Musa would stop doing things like researching Steel before I get to it, I would run over there and kick his ass right away. Instead, I'm just biding my time to hit him with a giant stack of modern troops right before he does something like research Physics. My best hope is to take all of his mainland cities and then make him a vassal rather than running around and capturing all of his crappy little island and tundra cities.
As per this thread, what I'm actually doing right now is having my Heroic Epic city and two other decent production but worthless commerce cities build up an army of Knights, Trebs and Macemen. (I would have skipped the knights, but I'm the Mongols, so with the extra XP from the Gers, the mounted units have extra appeal.) I've got a real nice ability to generate a lot of gold when I want to, as my commerce cities, especially my holy city, are very good. The plan will be to upgrade 20 trebs into cannons first, and then send them with the CR1 macemen though Ottoman territory to be prepared to hit the Malinese capital first. By the time those units have reached where they are going, I should have been able to generate enough cash to upgrade some of the existing knights into Cavalry. I'll quickly move them, as well as any Curirassiers I've built over to join the fray and this should make quick work of them.
After that, it's war, war, war all the way to the end. There's a lot of nice land to capture on this continent, and the other continent will be a complete pushover by the time I get there.