An active filter can have complex poles and zeros without using a bulky or expensive inductor.
The shape of the response, the Q (quality factor), and the tuned frequency can often be set with inexpensive variable resistors.
Certain circuit topologies may be impractical if no DC path is provided for bias current to the amplifier elements.
For some ranges of frequencies, for example at audio frequencies and below, an active filter can realize a given transfer function without using inductors, which are relatively large and costly components compared to resistors and capacitors, and which are more expensive to make with the required high quality and accurate values.
Since inductors are not used, filters can be made in a very compact size and do not produce or interact with magnetic fields that may be present.