Tom's Hardware ran a report two years back where they found that SSD's were actually using more battery. This is because actively they use always the same amount of power, while a HDD only uses high power if the head has to move across the platter.
Add to this a bit of housekeeping (garbage collection) and the SSD is even doing more work than the HDD would be doing.
I'm pretty sure that SSD's are doing better, power consumption wise, than two years but question is by how much.
HDDs use up to a few watts in active mode but that lasts very short. Idling they are very power-friendly. Keeping the platter turning also is not really much power intensive - the bigger issue is speeding it up from a sleep.
If we're seeing numbers of 15 watts to 12.5 watts (i7, nvidia vs intel graphics) then saving 0.2 watts by using SSD overall will not yield much battery saving.
Tom