Why to use a BJT transistor instead of MOSFET?
I would not make the generalization that MOSFETs can handle higher current and are more power efficient.  It very much depends on the application.

BJTs can be cheaper than FETs.  This is especially true for high voltage switching where the much larger die area of FETs make them much more expensive.  That's why you see IGBTs used for higher voltage motor controls.  IGBTs still can't compete with FETs for switching speed (the minority carrier issue) but often 20kHz operation is fast enough.

BJTs also have some differences from FETs than can make them more convenient in some applications.  BJTs start to turn on around 0.7V, where FETs mostly have much higher threshold voltages. For low supply voltages that can be useful. 

For high frequency power conversion with small magnetics the BJT can't touch the FET and FETs are now used almost exclusively in these applications.