Power consumption MOS vs BJT
I'll assume you're asking about power dissipation when both are used as a full-on switch.

MOSFETs look mostly like resistors when full on.  That's what the Rdson spec is all about.  The dissipation is therefore I2Rdson.

A saturated BJT looks largely like a voltage source.  For lowish currents (relative to the max capability), this is around 200 mV.  It can be around a volt for high power transistors at max current.  That's what the Vsat spec is all about.  The dissipation is therefore I*Vsat.

Whichever is lower depends on the specific parts and the current.

Generally, for transistors rated up to only a few 100 V, MOSFETS will dissipate less.  However, the Rdson gets worse with voltage capability, so above a few 100 V, BJTs usually win.

BJTs are also controlled by current, while MOSFETS by voltage.  Neither is inherently better, and each has its advantages.

The characteristics above have given rise to the IGBT.  That's a FET between collector and base of a BJT.  You turn on the FET with a control voltage, which turns on the BJT, which does the heavy lifting.  These can be good tradeoffs at voltages MOSFETs would have too much resistance at.  It doesn't take super low resistance between C and B of a BJT to turn it on, then the BJT can handle the real load current.  Note that when you're switching 500 V, a 1 V drop is only 0.2% efficiency loss.