Is this your homework? A perfectly insulated glass never sweats due to the drink inside of it. I suppose it could sweat if the glass itself was cold or if the rooms suddenly got hot and humid or something weird.

Ok, related: So let's suppose the 2 glasses have the same amount of energy absorbing potential, so in other words the same heat capacity and the same starting temperature. Look at a psychometric chart and see that cooling the air the first few degrees gets more water per degree cooling than the colder. This leads me to believe that the well insulated cup does better because the heat it is absorbing can more efficiently condense water. This simplification seems like it only works for 100% RH air. If the air is say 80F and 50% RH, the dewpoint is maybe 59 degrees or so? So if my cup is so well insulated that my dewpoint is never reached, I'm screwed. If I barely reach it, I'll condensate some but most of my energy is spent cooling air. If I get too cold, I'm inefficiently extracting water. An optimum should exist.

Alright, so: There are some issues here as the outside wall temp varies with convective heat transfer coefficient as well as overall insulation value. Let's assume outer material is constant and you just get better inner materials for insulation. That would mean pretty much that heat transfer increases linearly with outer wall to air delta T. For our case of 80F and 50% RH I get a graph like this which has temperature of the outer wall on x axis and a unitless efficiency number representing water per heat transfer. In this case, the optimum is a wall temp about say 40F.

So in general, I think the trend would be: in humid rooms use a well insulated cup and in dry rooms use the worst insulated cup and then there is optimums in between.