This may be the best description of difficulties I've seen. Granted as a strong Emperor/ weak Immortal player myself I view Immortal as time to get serious and Deity as "what did I get myself into."
If you can win sub-t300 you'll definitely be fine on King and likely Emperor too as long as you stay disciplined/focused.
I find that Immortal is not very challenging but Diety cheats so hard that it's not realistic game play anymore and thus not very fun. If only the AI could be good through actually good game play. That would be entertaining.
By realistic gameplay I mean doing things that are actually possible. Starting with 2 settlers and getting GL on turn 15 is not remotely possible and thus not something that is useful to practice against.