Not if made out of CMOS (and these days everything is CMOS). At steady state the only power loss in SRAM is gate and substrate leakage. Negligible.
> DRAM uses capacitors and only needs to be refreshed from time to time.
Yeah, 50 times a second. It adds up to quite a bit of power. Plus DRAMs have all the substrate leakage of the SRAM.
I'm pretty sure you're comparing supercomputer SRAMs from the early 80s, clocked to the limits of their lives, with low power modern DRAMs. If you compare equivalent parts you'll see that DRAMs are smaller but burn a lot more power.