On modern integrated circuits, are there as much BJT's on the chip as MOSFET transistor? If not, why?
It is very dependent on the circuit. See this reply on details why one would use one over the other:
For discrete transistors there are advantages to each. When we talk about ICs and VLSI systems the MOSFET is the device of choice because of the simpler manufacturing process and the fact that they are easier to miniaturize.
No, BJT has less extent than MOSFET because BJT is used where we need more speed. But MOSFET is used where we want less power dissipation, low operating voltage, less noise, simple manufacturing process, low chip area and easily scalable. Now, we use both devices as BiCMOS (BJT + CMOS) which has more speed than MOSFET and low power dissipation than BJT. Another main application of BJT is oscillators. BJT is better than MOSFET as oscillators.