BJTs have some benefits over MOSFETs for at least two digital applications. Very first, in high speed switching, they do not comprises the "larger" capacitance from gate, which while multiplied by the resistance of the channel provides the intrinsic time constant of the process. The intrinsic time constant places a boundary on the speed a MOSFET can operate at since higher frequency signals are filtered out. Widening the channel decreases the resistance of channel, but raises the capacitance by closely the same amount. Reducing the width of the channel increases the resistance, but decreases the capacitance by similar amount. R*C=Tc1, 0.5R*2C=Tc1, 2R*0.5C=Tc1. There is no way to minimize the intrinsic time constant for a specific process. Different processes by using different gate thicknesses, channel lengths, channel heights, and materials will have different intrinsic time constants. This problem is mostly prevented with a BJT as it does not have a gate.
The 2nd application in which BJTs have a benefit over MOSFETs stems from the first. While driving several other gates, called fan out, the resistance of the MOSFET is in series along with the gate capacitances of the other FETs, making a secondary time constant. Delay circuits make use of this fact to make a fixed signal delay by using a small CMOS device to send a signal to many other, several times larger CMOS devices. The secondary time constant could be minimized by raising the driving FET's channel width to reduce its resistance and decreasing the channel widths of the FETs being driven, reducing their capacitance. The drawback is that it raises the capacitance of the driving FET and increases the resistance of the FETs being driven, but generally these drawbacks are a minimal problem when as compared to the timing problem. BJTs are better capable to drive the other gates because they can output more current than MOSFETs, permitting for the FETs being driven to charge faster. Several chips use MOSFET inputs and BiCMOS outputs.