I won't argue how the game feels, Renata. Several changes make C3C here either harder or easier, depending on the map or your playing style (scarcity of resources, map/contact trading, SoZ etc).
But from the 'raw' settings, like AI production boni, corruption, goody hut outcome etc, vanilla Deity is pretty much C3C DG.
There is one big reason why C3C is more difficult, under otherwise identical circumstances: The new corruption model, which helps the AI a lot. No more RCP, no more second core - even field here. Throw in AGR, a Civ trait that really helps the AI, and you can get such killer AI Civs in C3C as never imaginable before (Sumeria...).
Of course, we're all more experienced now, so we hardly notice. And, for me, being a trader and AI manipulator at heart, C3C is indeed easier.
But, that doesn't have to say much - comparing DyP to RaR (which both have the delayed trades) is clearly a lot easier.