What is passive EQ compared to an active EQ circuit?

A passive EQ uses inductors and high value capacitors to filter; there are no amplifiers in the circuit to filter. It uses an amp to match impedances. An active type EQ circuit is different in that the filter (reactive) element is located within the feedback loop of an amplifier. These generally utilize lower value capacitors and resistors instead of inductors.
One of the main advantages of passive EQ's are in the way they sound, which tends to be more musical due to rich harmonic structure inside the inductors. Another huge advantage is the excellent phase coherence exhibited by this type of circuit. Active EQ's tend to have strange and unpredictable phase discrepancies around the EQed frequencies, making the sound somewhat smeared and unfocused, whereas a passive circuit will not have this effect. Disadvantages for passive circuits include the cost as the inductors need to be very high quality with strict tolerances, the capacitors need to be very high value, and aligning the unit is time intensive with slight adjustments in gain and impedance to tune all the frequencies. Also, inductors change thermally so frequencies can drift slightly, although seldom more than 1/8 of an octave. Generally larger components are needed as well, so size can be an issue, although the FeQ-50 is remarkably small for a passive LC circuit.
Active EQ circuits tend to cost less as resistors are much cheaper than inductors and the capacitors need to be much lower value. There is also very little thermal drift so they can be very accurate and precise, a good thing for a 'fix-it' EQ. The thing to watch for with active EQ circuits is the phase coherency and transient intermodulation distortion.