Basically , all are constructed for the main purpose "AMPLIFICATION",
but
mainly there are some parameters differentiating them.
1.Gain: For BJT you will get a good gain, but the problem is,it consumes the current from the source causes you are obtaining gain by loosing some thing (power).
But in MOSFET the same gain you will get by zero input current.
2.Physical parameters: Your BJT area is not a matter for amplification (of course you won't consider it), but in MOS area of MOS is the main parameter .
3.MOS is better immune to noise than BJT. BJT mostly suffered by thernal noise.