Well, we forced ourselves to win this one a certain way and it still had that effect.
Typically, as players we work on exponential build-up, so that once we catch the AI, we leap ahead and win. It's that period of equality that is most interesting -- or being slightly behind.
Harder difficulty levels tend to move that period of time where you're equal to later in the game, so you can experience wars (or whatever) with different units, but you run the risk of getting crushed early before you can get anything going.
Probably the best game I had for consistent struggles was the Progressive Paranoia game I ran back in Civ3 days. Each age brought new restrictions on how we could play, so by the end we were at war with everyone. Definitely artificial restraints on how to play the game, but they seemed to work well. I'm not sure Civ5 can be so constrained....but maybe.
It's a perfectly fine topic and it's now as on-topic here as anything else, so I'm happy to continue discussing it.
Arathorn