You're absolutely correct. What counts is the "watts".

The real issue is the technology and the confusion tends arise with halogen lamps, because you find these in both high voltage and low voltage variants. Both are power hungry. A 60 W halogen lamp will consume 60 W whether it's running at 12 V or 230 V (indeed probably a little more at 12 V, because there's a transformer in between which will take its small share).

There are however energy efficient low voltage lamps too, notably the new generations of LED lamps. It's still a new technology, but one which definitely has a big future in front of it.

At Leonardo ENERGY, Stefan Fassbinder took the effort some time ago to document the effect of voltage reduction on energy efficiency for 7 electrical applications, mainly in lighting:

Follow this link

One of the other alternatives is the small diameter florescent tubes.  Carefully chosen, they are more efficient, with spectral output closer to sunlight. 

One of the overlooked issues with LV lighting, if voltage reduced then the current must go up to keep power constant.  The problem is that when this is done, there is resistive heating in the wires.  Copper is not a perfect conductor and heat goes up by the square of the current. That is for a doubling in current the heat goes up four times!  Once again we are faced with trade-offs.  -doug

All of the above aspects are correct. But, a few words from me. Here the question is whether 'Power Saving in Low Voltage?'. Yes, there will be. Not in the aspects explained above. But when we use the Low Voltage Devices. We know when a distribution system carry high current for the equipment, surely there can be voltage drop in the cables/wires due to the high current comparatively. But, with the devices such as LED, OLED, etc. only low current flows. Then, the drop loss will be less comparatively, which could be an added advantage of the Low Voltage? Could it be counted as a Power Saving? (Just for an Arguement!)

Low voltage lighting saves power because low voltage lamps (I mean here halogen incandescent lamps) have a higher specific light output (lumen per watt)  than mains voltage lamps of the same technology (halogen incandescent).

A 50W, 12V halogen lamp will thus yield more light output than a 50W, 230V halogen lamp. Less power is thus needed for the same amount of light. Hence the opportunity for power savings. As usual, there is the tradeoff with transformer losses, resistive losses in the leads due to higher currents, etc.