Current consumption in a MCU depends on four things, basically.
- Supply voltage (not always)
- Operating frequency
- Enabled Peripherals and their clock speed
- Actual firmware
2 and 3 are obvious, since the current consumption in a FET gate is proportional to its switching frequency
Actual firmware may suprise... or not, because different instructions require different gates to be switched, also different number of memory access, etc.
Then, while current consumption ALSO depends on applied voltage, most if not all modern MCUs may be operated at 5V, but their internal core logic is running at a much lower voltage, tipically 3V3,1V8,1V0, ... usually using an LDO, so between some range current consumption is almost constant.
Those without internal LDOs (Like PIC16LF) have the core supply directly tied to VDD, so their current consumption IS greatly dependent on applied voltage, they can also run at lower voltages because there is no need to have a minimum VDD for the LDO to operate correctly.