Ha! Curtains. I know curtains because I built a pretty comprehensive bespoke curtains website a few years ago. I could bore you with all sorts of details but I'll just say that the extra width you mention is called a "fullness factor", and was set to 1.5 for tab-tops, 1.75 for eyelets, and a massive 3.0 for box-pleated curtains. It doesn't really get more exciting than this, does it?

As for your question, choosing the interlined option would be recommended in order to increase insulation. But seriously, curtains - interlined or paper thin - are not very effective at stopping heat loss. They don't fit closely enough to give effective insulation, so spending time on the window and walls would come a long way in front of curtains. Having said that, if I was going to try to use a curtain specifically for insulation, I think I would want it pinned around the window on all four sides. I'd want it as thick as possible and if it prevented air-flow then so much the better... it's starting to sound like triple-glazing...

Without in any way challenging Pete's cortinal expertise, I think that he is a little unkind about the insulation value of curtains. Good heavy curtaining certainly is less effective than alternative schemes that require less material and lower cost, but it interferes quite persuasively with patterns of convection and radiation, especially if it is lined with light-coloured material. (This is especially important in warmer countries, such as South Africa, but one feels it in cold weather as well.)

There are of course subjective effects as well; a well-curtained room looks cooler in the heat and warmer in the cold. For the best effects of this kind one needs luxurious material, deep pleating, and full length drops.There are of course other useful effects, such as the mood-enhancing influence of well chosen placement and designs, and the dramatic difference in acoustics, particularly the damping of irritating high-frequency echoes.

Technically curtains are disastrous insulators but the purpose behind a curtain is to stop convection currents. If the curtain was not present what would happen would be the air at the window would cool more then the rest of the air in the room causing it to sink and push more warm air across the cold panes of the glass, thus making a sort of fan almost. The fabric of the curtains is an insulator and therefore does not take the heat of the air so such a high degree. The pleats or folds in the curtain help this effect by not allowing the air a straight surface to create a nice circular movement, instead what happens is the air will be deflected at an angle and therefore leading to a smaller current, or at any rate not drawing the warm air of the room towards the window but using the same cool air that is already near it.

To shorten my answer and solve your argument, yes the extra folds are more efficient then a straight blind.

I have some comments on the above, assuming the moderators will excuse me for commenting on my own question!

To petethebloke: am I right in inferring that box pleating means that adjacent pleats touch each other? If so, this would trap cylinders of air which one would expect to make a significant improvement. What would be the best way to prevent air leaks round the edges, however? 

To Jon Richfield: I have used curtains to shut out direct sunlight, but I'd forgotten that what keeps heat out may also keep it in! Seeing that a dark night sky would act as a giant heat sink, radiation may be more important than one may think!

Dry.

Glad to reply. I hope you'll forgive me a slightly misleading answer before. The box pleat is sewn only into the pelmet not the curtain itself. See attached picture. The "most-pleated" curtain is the triple pleat, which uses a fullness factor of 2.0.

In my experience (and remember, I made the website, not the curtains) a good quality, interlined floor-length curtain, is a pretty good barrier. For a start, they weigh a ton! If you extend them wide of the window on each side, and make sure they just meet the floor, then they really are quite effective. In scientific terms, triple-glazing and wall insulation would be better at retaining heat. More practical but less attractive.

As for tab tops and eyelets? Just a passing fashion!