And, once they become more popular, mods.
I've only had time to play and finish one entire game, but started a few others (hope to get some time to finish another tomorrow!). TBH I don't remember the first game's difficulty, something lower than Apollo. But the ones I've been messing around with since then have been on Apollo, and I finally found out how to get to the summary screen. Been on par with research and tech, and I wasn't playing anywhere near optimal.
So the other thread here comparing Apollo to Emperor is probably correct. But the one extremely important thing to add is there is no NC and great scientists in BE, which means balance between a highly focused science empire and a regular empire is going to be much closer. And unfortunately in an "equal", the poor AI really begins to show. In other words, since the player isn't forced to play NC gymastics for the first 80 turns and can get straight into the game right away, it is exposing the weaknesses of AI even more.
Deity challenge in CiV was largely an illusion. Once you get to mid-game and you don't need to ignore everything but science, AI still sucks. Since you can be competitive in BE without ignoring everything else, you just reach that point much quicker. The artificial difficulty has essentially been removed, which is why Apollo is no where near the same experience.