The ability of a material to insulate depends mostly on 2 factors: the thickness and the thermal conductivity. For the best insulation, one would want higher thickness and lower thermal conductivity.
If you have 2 cups of equal thickness, one glass and one plastic, the plastic cup will insulate 5-10 times better than the glass cup, because the thermal conductivity of plastic is 5-10 times lower than than that of glass. The physical reason for this is that glass has a more regular atomic structure than plastic does. This allows heat to transfer faster in glass than plastic.
From my experience, glass cups are thicker than plastic cups, possibly 5-10 times thicker. Because of this, I would expect that glass and plastic cups can insulate relatively equally.Thank you!