Why are MOSFETs better than BJTs in application of Voltage Controlled Resistor?
The following refers to NPN BJTs and N channel FETs

It's really hard to get good accurate representations of collector current versus collector-emitter voltage for different levels of base current. It's a bit easier for JFETs because, traditionally they claim to encompass the functionality of a voltage controlled resistor. Anyway, here are the best three I could find and they show a similar story: -



Top left is a BJT. Top right is a JFET. Bottom left is a MOSFET and bottom right I have drawn my own picture of the saturation/ohmic region. Basically, what I'm trying to say is that all three devices can be used as a voltage controlled resistor (VCR) because the base/gate control can vary the slope of the graph and the slope is basically conductance and that, in turn translates to resistance.

One thing that makes a JFET much more superior is that the drain current and voltage can be reversed (made negative) and the characteristic shape of the resistances are largely similar. They are not hi-fi quality the same but good enough for controlling volume in a cheap transistor radio or amplitude in a sine wave oscillator. 

BJTs wobble a tad when the voltage is reversed because you are then relying on the transistor being symmetrical and having the same gain. MOSFETs usually (but not always) have a parasitic diode which makes them unsuitable for negative voltages when used as a VCR.

I'd go for JFETs every day.

As a footnote don't believe that the BJT characteristic looks like this: -



It completely fails to show the ohmic/saturation region properly, Rather, it seems to indicate that there is a one value of resistance irrespective of base current.