For a long time, I didn't understand why someone would use a BJT unless they needed drive capability at low voltages. But, as I get used to BJTs I'm starting to see their advantages. Each has strengths and quirks.
BJTs conduct in more ways than MOSFETs do... you can conduct either way between the base and collector on an NPN for example, but the gate and drain of an N-channel MOSFET seem to be more isolated. (Someone correct me if I'm wrong here.) So you might need to watch out for current flowing in unintentional ways when, for example, a pin isn't being driven, or in a fault scenario. OTOH, this behavior can also be useful.
Then there's cost... When searching for low-current switches (like <100mA to PWM an LED), Digikey seems to have lots of TO-92 NPNs for less than $0.50 in single quantities, whereas N-ch MOSFETS are a bit more expensive -- in many cases, closer to $1.00.
The circuit might also be simpler. Check out the first half of each set in the attached image. For a MOSFET, you should usually have a pull-up or pull-down to set a reference voltage when the drive pin is high-Z. With BJT, a high-Z pin should not conduct current, so it should remain off. (More experienced guys -- any qualms with this?) However, most people advocate using a series resistor to limit current draw from gate capacitance with MOSFETS. So you're using two drive resistors instead of one.
Now, referring to the second half of each set, if you're using an NPN-PNP pair (to switch a higher voltage on the positive end with logic HIGH = ON, for example), you may be able to economize further by limiting the current that can flow through the PNP's base by limiting the drive through the NPN. With a 150K resistor on the NPN base, and a gain of 100, it's at the sweet spot for the PNP with no need for a current-limiting resistor on the PNP. Although the success of this approach depends on the actual gain of the BJT, which is sometimes not quite what is specified in the datasheet. You would have to be wary of parts tolerance, or go the safe route and just add one more resistor. The latter is probably a better approach most of the time, but if parts count is the priority, you have the option...
The biggest difference of course is that BJTs are current-controlled, and MOSFETS are voltage controlled. There are applications that make one more suitable (or convenient) than the other, and if you're comfortable with both, you can choose the one that is the best fit instead of shoe-horning the part you have and understand.