Generally speaking, thermal curtains are more likely to help control the temperature of a room than vertical blinds. But the main dependent factor is the insulating ability of the window treatment. There are ways vertical binds can be made to give them more insulating ability.
How Insulation Works
Air is a good insulator. If you have a layer of air trapped between two layers of fabric or vinyl, it will be a better insulator than one layer of the same fabric or vinyl by itself. Because of this, any type of window treatment that has more than one layer will be a better insulator than something with a single layer, and more than two layers will insulate even better.
R-Value: Measurement for Insulation
R-value refers to the ability of an object to resist the flow of heat. The higher the R-value, the more insulating an item is. Insulation you put within your walls or in your ceiling probably has an R-value somewhere above 40. Window treatments can have an R-value from 0 to 5, though not all window treatments have a rated R-value.
What Makes a Blind a Good Insulator
Two features of a window blind influence its R-value. First, more layers mean more insulating ability. Vertical blinds made of PVC vinyl or a single layer of fabric will not insulate as well as vertical binds that have vanes with a pocket of air in the middle. The second feature influencing R-value is how tightly the blinds fit against the window. Since the vanes of vertical blinds are meant to swivel, they will need room to do so. Wider vanes will need to be mounted farther from the window frame and will therefore leave a bigger gap when closed. Vertical blinds can have an R-value up to almost 4.
What Makes a Curtain a Good Insulator
As with window blinds, the number of layers and the quality of the fabric a thermal curtain is made from will affect the R-value of the curtains. Thermal curtains are made with multiple layers so they have this quality built in, though individual varieties will have a range of R-values. The way the curtain fits around the window frame is another factor. Any gap around the edge will lower the curtain's ability to adequately insulate the window, so the best is a curtain that fits snugly around all sides of the window. Window quilts and draperies can have an R-value of anywhere from 3 to 5.
Windows can leak heat because air may pass around ill-fitted glass. Caulking and weatherstripping can reduce this problem. Double-paned windows have more insulating value than single-paned, due to the layer of air between the two panes. Insulating curtains or blinds can increase the insulating value of any window, but won't prevent a draft that can be fixed by caulking or weatherstripping.
Best Use of Window Treatments
Whether you have curtains or window blinds, they work by preventing the transfer of heat. In winter, you don't want the heat from indoors to leak out, but you want the sun's warmth to come in. So it's best to keep the curtains or blinds open on sunny days, and close them at night to prevent heat loss. If it is bitterly cold out, you may want to keep them closed all the time, especially on north-facing windows. In summer, it's just the opposite. Close the blinds or windows during the day, to keep the heat out. If you don't have air conditioning, open the windows at night to let the cool night air in.