If you are doing any timing related communications outside the microcontroller (serial, pushing spi to limits, etc) or keeping time or whatever then you need a more accurate clock.
It is not really about power, marginally perhaps, if the clock is a little slow then you use more power if a little fast then you save a little power.
Many but not all microcontrollers offer an internal R/C oscillator so that you dont need to have an external oscillator (extra components, extra cost). This is not one family vs another (avr, msp430, pic, etc) some chips within a family have internal oscillators some dont. The PIC's I used back in the day required an external, dont know the family in that detail today. How the calibration happens also varies from family to family.