What is the ON resistance of a BJT like a 2N3904?
BJTs have a saturation voltage. That will vary a bit with current, but not linearly so you would speak of a fixed resistance. The voltage is much more constant than that. 



This graph from the 2N3904 datasheet shows a typical saturation voltage around 50 mV between 1 mA and 10 mA collector current. That's typical, but elsewhere in the datasheet it says 200 mV maximum. If your ADC reference is 3.3 V that can give you an error of up to 6 %. Probably less, because that's when the resistor ratio is very large. With both resistors equal you'll have a 3 % error. It's up to you to decide if that's acceptable.  

A FET will do much better. What you need is a logic level FET. There's plenty of FETs which will fit your application. The Si5406CDC, for instance, has a \$V_{GS(th)}\$ of 1 V maximum and an \$R_{DS(ON)}\$ of less than 20 m&Omega; at 3.3 V gate voltage, which is negligible.