What difficulty level are you refereing to here? And do you mean powerful by flavors, or has grown to be powerful over the course of the game? If you mean the latter, then you need to prevent that in the first place.
Deity of course. I find it pointless to even try any other level in this game.
Of course you often can often easily defend your borders against a powerful AI, but the catch is that he will never discuss peace with you as long. In earlier versions of Civ, and especially Civ 4, wars were really expensive. If you couldn't penetrate your enemy's defense for 10 turns, your people would get really angry and the cost of the troops would hurt your income, which could lead to that you fell behind in the tech race. Therefore it was always advisable to make peace if a war wasn't going anywhere.
In Civ 5, these penalties don't exist. The AI work like this: "Okay, the player has 10 units, I have 30 units, good, I will eventually win the war so I shouldn't discuss peace". The result is that I often find myself in constant war with two or three AI's, which isn't fun at all, even though it's quite easy to trick them into my traps.
The big difference is between Civ 5 and earlier games is that Civ 5 focuses much more on the actual battles and much less on the planning. Even though the SoD itself didn't need very much thought, there were big decisions to be made
before the war. The question wasn't just "Will I be able to destroy the AI", the question was "Will I be able to defeat the AI in an acceptable amount of time". When I began playing Civ 4, some of the wars I declared really ruined my game even though I was stronger than the AI, because war was more a matter of economy than battle strategy.
And this is the difference. Shafer wanted to do the battles more fun be removing war weariness and such. But the result is often that you fight until one gives up. And this is not fun.