That sounds like a question more suited to its own thread, Sparky...
What I expect/desire:
1. Seamless blend with the mains (implies good amplitude and phase control at the crossover point, and ideally variable crossover slopes);
2. Frequency extension to 20 Hz or below (mine is down about 3 dB at 14 Hz, 6 dB at 10 Hz) and well above the crossover point (perhaps an octave) to allow for finite LPF slope;
3. Sufficient amplifier power to not limit the system (important since bass often requires much more power than mid/treble);
4. Impulse (time-domain) response matching or better than the mains (particularly with low-distortion speakers, which encompasses most panels but also quite a few conventional designs these days). For me this has for decades required a servo design to be practical for me; as an aside I find that "speed" is meaningless in a sub, but a sub that rings well after the initial impulse sounds "slower" and "muddy" to most listeners; and,
5. Reasonable size, weight, feature (control) set (mine includes gain, continuous phase, and a single-band PEQ).
FWIWFM - Don