So why do SSD disks have a reputation for power efficiency?
There might be few things to consider as why SSD have a reputation of higher power efficiency. For example, compare WD 2.5" HDD "black series" with Samsung 860 series SATA drives:

WD, 250/500 GB:



Samsung 860, same 250/500 GB:



First, as one can see, Idle for HDD is 800 mW, while idle for SSD is 50 mW, or HDD consumes 16X more. Note, that most time the drives in PC idle. So we have 16 X power savings already there, roughly speaking.

Now, power during read/write operations is listed as 2 W for HDD, and 2.5 W for SSD. However, write performance of 2.5" HDDs is about 25% of SSDs, see WD wd5000lplx report as compared to Samsung 860 report. Sustained sequential reads/writes of 2.5" HDD rarely exceed 120-130 MBytes/s, while SSD makes steady 500-550 MBytes/s. 

It means that if you have an application that transfers certain amount of data per second, the SSD will take only 1/4 of active time as compared to HDD. Therefore effectively the SSD will use 0.5 W where the HDD will use 2 W.

I think this is a good reason to designate SSDs as ~ 4X more efficient than equivalent HDDs. (Disclaimer: few times in my career I supplied benchmark data for marketing, so please forgive me for some stretches :-))