"sophisticated conversation" is correct and usable in written English.
You can use it any time you want to emphasize that a conversation is characterized by intelligence, knowledge, or culture. For example: "We had a sophisticated conversation about the intricacies of philosophy."
"It was a very energetic, sophisticated conversation about global threats".
"Parents should not wait for the sophisticated conversation of a teenager".
If nothing else, The Cyber Effect should enable us to have a more sophisticated conversation about it.
That was never true or accurate, but the new situation made it even more clear that we needed to have a sophisticated conversation about migration and race.
Clearly, the nation and first of all the Democrats could use a better, broader, more sophisticated conversation about religion and politics.
The congressional senior aide, who was centrally involved in negotiations over the bonus tax, said, "One of the problems with this Administration is it has tried to have a grownup, sophisticated conversation with the public.
Whitebox's offices feel like a high-tech dorm room, albeit one with notably more sophisticated conversations.
We need more sophisticated conversations about privacy with the companies harvesting our data from these devices, say commentators.
Drunk Russians in bars or on the battlefield hold sophisticated conversations about whether or not the world really exists, and what the meaning of death might be.
The rise of the London-based Chinese professional has less to do with an ability to write coherent sentences or conduct more sophisticated conversations – than their UK counterparts – than a willingness to apply their training, work all hours and submit to Victorian management practices.
"And the amazing thing is that these quite sophisticated conversations are now happening all over Ireland: what was the Rising, what was it about and what does it tell us about now?" So there is severity and sincerity beneath today's march past the GPO and the carnival tomorrow which Irish television RTE calls "the biggest public cultural and history event that has ever been staged in this country".
