Mostly yes: mirrorless cameras use more power because they must keep the sensor and a display active almost all the time for framing. An EVF or rear LCD needs continuous power, and the sensor has to be read continuously to feed that live view. In a DSLR, the optical viewfinder uses essentially no power for composing, and the sensor usually only powers up for metering, autofocus, and the actual exposure.

Another common reason is battery size. Mirrorless bodies are often smaller, so they typically use smaller batteries with lower capacity than many DSLRs. That means even if efficiency were similar, they may still deliver fewer shots per charge.

Since you already shoot heavily in Live View on your DSLR, the gap may be less dramatic for your personal use than for someone who mainly uses the optical viewfinder. But in general, mirrorless still tends to have shorter battery life because live view is always required.