It's difficult to say because every game is a qualitative experience, not quantitative. On Emperor lately, since the patch, I've struggled a little (usually against Hiawatha, who, as I said before, seems a little out-of-whack in terms of out-teching and out-producing everyone by a wide margin on Emperor).
Yet I fired up Immortal a few days ago, and won without too much trouble (relatively, considering I'm probably just an Emperor level player). In that game, I drew a spot of terrain where I could get 4 cities up, yet had a reasonable defensive position due to surrounding city-states and mountains. I was the Aztecs, had every city on a river for the UB, and grew super tall while only taking one or two DoW's in the entire first 150 turns.
Then I turn around and play Emperor today, and Hiawatha on the opposite end of the Pangea has a mysteriously large tech lead early on and I struggle for much longer than usual and barely win by turn 390 or so, when I usually beat Emperor a hundred turns earlier.
There's just too much else that goes into why a particular game is harder or easier than it usually is on the difficulty level you've selected. I have to agree with Buccaneer and Browd, though, that since the patch, the difficulty levels are still not perfectly consistent in terms of challenge, and moreover, that it'd be almost impossible to have a fair comparision with all variables controlled for other than the patch itself (pre-patch vs post-patch).
What I will say, since the patch, is this:
1) on both Immortal and Emperor, the AI seems to have a slight better ability to use its gold, as others have said
2) again, on both difficulty levels, I seem to run into larger navies than I remember, which is a good thing (pre-patch on Emperor especially I remember not seeing much in terms of AI navies)
3) DoW's are still about the same. I've played a few games on both levels since the patch, and echoing Browd in admitting 3 or 4 games on each level isn't enough to say for sure, I'd have to say that Immortal I usually still take a 2 or 3 civ joint DoW by turns 100-120, whereas on Emperor it's still pretty unusual to have more than 2 civs DoW me at once unless I'm far enough ahead and conquering cities in numbers.
And I agree that Emperor is a good level for the average knowledgable player to be at. When I beat Immortal, it's usually a bit of luck on a good roll, and when I've beaten Deity those two or three times, I was really taking my time to evaluate each turn along with again having a good roll for terrain, city-states, enemy civs, and so forth. I normally play Emperor (~70% of games I played in the last year) and play Immortal sparingly (~20%) and Deity rarely, when I feel up to a good challenge and don't mind a probable loss (<10% of the games this last year).