I'd go group delay first as it is no use having low distortion if there is a whole load of resonance or ringing from your sub - remember your room is going to resonate too! So less resonance or the sooner the sub stops ringing (overdamped) the better IMHO. Ideally you want both low group delay AND low distortion AND high SPL output but it is expensive to get all three...
a good rule of thumb is less than 25 ms group delay at 20 Hz This corresponds to 20 feet added distance between something you hear at 20 Hz and its upper harmonics at 80 Hz (which may only have a 2 msec delay). It is probably not audible at this level so bass will be nice and tight and sound integrated with the rest of the music (kick drum is real tangible and there). Delays of 50 msec are probably becoming audible (nearly a full cycle) but this is all hotly debated. The problem is that the tweeter sound of the kick drum beater hitting the skin may last a mere 2 msecs - so if the deepest sounds arrive delayed by 50 msec then it is going to sound like delayed room or concert hall reverberation rather than the instrument itself - so while this may be an added and pleasing effect on dinosaur footsteps it may cause the kick drum to sound distant and less "integrated"or lacking "punch". (You can look up Hass Effect to understand how our brain separate sounds that arrive much later - we simply interpret these late arrivals as being reverberant reflected sounds and NOT the primary sound.)
As a rule of thumb, ported subwoofers generally have twice the phase shift and twice the group delay of sealed subwoofers and oscillate twice as long after the signal stops. That is why I claim that "as a rule of thumb" sealed subs will be tighter and better sounding even if they have poor SPL output. (Of course a ported sub that is tuned way way low at 10 or even 5 HZ is likely to sound pretty damn good and close to sealed sub - so it is only a "rule of thumb")
a good rule of thumb is less than 25 ms group delay at 20 Hz This corresponds to 20 feet added distance between something you hear at 20 Hz and its upper harmonics at 80 Hz (which may only have a 2 msec delay). It is probably not audible at this level so bass will be nice and tight and sound integrated with the rest of the music (kick drum is real tangible and there). Delays of 50 msec are probably becoming audible (nearly a full cycle) but this is all hotly debated. The problem is that the tweeter sound of the kick drum beater hitting the skin may last a mere 2 msecs - so if the deepest sounds arrive delayed by 50 msec then it is going to sound like delayed room or concert hall reverberation rather than the instrument itself - so while this may be an added and pleasing effect on dinosaur footsteps it may cause the kick drum to sound distant and less "integrated"or lacking "punch". (You can look up Hass Effect to understand how our brain separate sounds that arrive much later - we simply interpret these late arrivals as being reverberant reflected sounds and NOT the primary sound.)
As a rule of thumb, ported subwoofers generally have twice the phase shift and twice the group delay of sealed subwoofers and oscillate twice as long after the signal stops. That is why I claim that "as a rule of thumb" sealed subs will be tighter and better sounding even if they have poor SPL output. (Of course a ported sub that is tuned way way low at 10 or even 5 HZ is likely to sound pretty damn good and close to sealed sub - so it is only a "rule of thumb")