For simplicity we'll say 'thin' and 'thick'.
There's the formula for Henry value of an air coil, given coil diameter, length, number of layers, number of turns. To what degree are these parameters affected by thick insulation? The wires are separated a small distance, but what is the overall impact?
As for the core, it delivers the advantage of reducing number of turns, thus reducing copper resistance.
Theory suggests...
For greatest efficiency the wires should be as close as possible to the the core, enabling tight interaction between core and flux field. In that manner thick insulation hampers inductance.
Practically speaking however...
It's not hard to wind a few additional turns to make up for the loss.