You got peanut butter on my chocolate.
Your chocolate got in my peanut butter.
But getting back to idiograms...
While it is far from the case that idiograms are strictly pictorial in nature, I do think that for a vocabulary of marginal literacy, idiograms are somewhat representational. So one could have a fifth grade level of literacy in an idiogramatic writing system much more easily than one could have a fifth grade level of literacy in an alphabetic writing system.
In order to acquire a basic written vocabulary in an alphabetic writing system, one has to acquire all the same tools that are used in the advanced vocabulary: learning the alphabet, learning the phonemic overlay to the alphabet, learning all the idiomatic spellings etc.
Even where idiograms are not representational, there is nothing systematic to learning a symbol that builds a comprehension of other symbols as there is with an alphabet. It makes the alphabetic system more powerful in a way, but means there is a higher investment in acquiring the alphabet. My guess is a wider range of people are literate in an idiomatic language, while literacy was very restricted in Europe during the Middle Ages.
So I'd disagree that the timing relative to being written down determined the divergence of Chinese languages vs. European ones. I'm still thinking about it, though.
Are they still teaching in linguistics classes that writing systems are not really a linguistic question?