Virtually impossible to assess but a side by side test would be fascinating.
I suspect that the simple logic that a laptop uses less power than a desktop is subject to whether it's used on battery or not -- recharging batteries is doubtless incredibly inefficient.
There are of course other issues than power in comparing cost of ownership.
Laptops generally give less bang for the buck than a desktop.
Repairs can be far more expensive -- in fact a desktop can usually be fixed for the price of generic components. A laptop will usually need a specialist repair, often using proprietary parts.
Though people often keep laptops for longer than desktops (I suspect because they cost more to replace) upgrading more than just the memory and hard drive is virtually impossible, so the performance of the laptop cannot be upgraded to the same extent as a desktop -- the desktop actually remains useful for longer.