"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.
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.
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.