from http://www.differencebetween.net/technology/difference-betwe...
Because of its lower price, DRAM has become the mainstream in computer main memory despite being slower and more power hungry compared to SRAM. SRAM memory is still used in a lot of devices where speed is more crucial than capacity. The most prominent use of SRAM is in the cache memory of processors where speed is very essential, and the low power consumption translates to less heat that needs to be dissipated.
In any case, SRAM can be more power hungry that DRAM (per bit) but it can also be vastly less. SRAM power consumption is not at all driven by the fact that registers are "continuously powered". Accessing SRAM is the power hungry operation, but powering requirements otherwise are negligible. If anything, it's the DRAM that requires constant powering (refreshing).
