3.3V is indeed the "everything" voltage. Why should I prefer a BJT in that case?
It's not enough to saturate "logic level" MOSFETs that are rated Vds > 20V or so.
Lower voltage MOSFETs have higher gain, with 6-10V parts being 1.8V logic level compatible; some are available in battery-management-scale parts with Rds(on) < 1mohm!
Gain quickly drops to ordinary levels as you go up in voltage. Hence there's no need to go over about 10V drive, for MOSFETs rated 30V to 2500V+.
"Logic level" MOSFETs, at regular voltages, are just regular devices modified for lower Vgs(th). Their performance is marginal at 5V, because Rds(on) isn't quite saturated at that level, and the lower gate voltage takes longer to cross the switching threshold. It's good enough for simple things like relays, but I don't recommend it for power switching applications.
AIUI BJT switch will consume more power (current) as I will need some Ib to keep the transistor on. Whereas with the MOSFET the transistor doesn't consume/dissipate power during the on-time, only during the transition off-on and on-off. But in that understanding I'm not considering the voltages of the switch device vs the load.
As long as I am operating in the linear/ohmic region of the MOSFET (which I am; Vgs-Vth > Vds), I would have thought that I am good. What am I missing here?
Look at it by overall efficiency: you're spending < 1/10th the current, and 0.7V, whereas the load might be dropping well over 7V. That's over 40dB power gain already!
BJTs get less attractive if the load is externally powered, and internal power is limited (e.g., a battery powered device with contact closure output), or if the load current varies and isn't always at high current (in which case you're wasting all that base current for no reason, most of the time).
There are some ways to arrange a circuit to deal with this, for example drawing parasite power from the load during the off state (a few uA will be nothing but leakage for most applications, but could be sufficient to keep the battery topped up), or controlling base current to keep collector voltage just barely saturated (the Darlington is a simple arrangement of this, but Vce(sat) is rather high; more creative arrangements can achieve better saturation, and with less current consumption and more speed).
BJTs start looking particularly attractive at low voltages, particularly in applications that can spare the base current. Battery powered switching regulators are a good example: if it's always operating at design current output, then efficiency will be high -- you don't much care about base driving power exactly, as long as overall efficiency is good. Switch outputs from non-micropower, low voltage ( <= 3.3V) logic is also a good candidate: the BJT will save cost, switch better from the logic source, and you don't mind the base current.
Low voltage and low-Vce(sat) BJTs also have improved hFE, so that you can switch them at hFE(sat) = 50 or 100 even. When you're doing this at power switching frequencies, you're mostly delivering turn-on and turn-off current -- because the base-emitter junction is charge-controlled, just like the MOSFET is. The BJT starts to look more like a leaky MOSFET with super-high gain, than a BJT!
Tim