When idle, the CR1000, CR6, and CR1000X consume less than 1 mA @ 12Vdc. Similar to the CR6, the CR1000X has a much faster processor that requires more power when up and running. As such, there will be higher current draws during active measurements, serial communications, or when plugged into a PC via USB or Ethernet.
It may be helpful to think of the CR6 and CR1000X as being built on the same "platform."