DAB radios do consume a lot more power than am/fm - it can be a factor of 3+.
DAB requires a lot of signal processing to decode the digital signal and the early radios used quite power hungry general purpose DSP chips which were programmed to perform the processing. Most major radio chip manufacturers, other than those producing cheap Chinese radios, are working on reducing the power consumtion to perhaps 25 to 50% more for DAB using dedicated signal processors. I believe the UK radio manufacturer Roberts Radio is leading in this field.
Of course the difference may be overshadowed by the power being injected into the speakers at high volume.
