I've had three different sets of subwoofers in my primary system and each has sounded different for music. They were all positioned in nearly the same locations, with small adjustments made for each in order to achieve the smoothest frequency response. I'll start with the disclaimer that all subjective impressions were done sighted and I did not possess the benefit of being able to switch instantly back and forth between them. I am not sure how one is supposed to accomplish this when dealing with massive boxes that are highly sensitive to room placement and calibration.
The space approaches 6000 cu ft and sits on a carpeted slab. All measurements were taken at the MLP, roughly 11-12ft distant from each sub.
The first pair of subs in this room were Hsu VT3 MK5s, run with 1 port plugged in extension mode:
I used these for many years. For music, I thought they sounded great. At higher volumes they could sometimes sound a bit strained and would introduce port noise with content that reached below ~25Hz.
Then I moved to dual Monolith 15" V2s, run with 1 port plugged in extension mode:
These clearly extended further, and essentially eliminated the occasional port noise issue. They sounded "cleaner" overall and could be run much louder without complaint. They also seemed to put more tactile energy into the room. As a result I felt a clear preference for these for music, though it was rather a modest one. Most of the benefits of this upgrade manifested in home theater use.
I then replaced the Monoliths with PSA TV2112Ms:
Below 20Hz these really benefitted from room gain. I didn't bother to EQ this region down, because for music it's rarely intrusive and for home theater that's simply "free" headroom.
As you can see, all three sets of subs presented a reasonably flat frequency response post-calibration. They were all in the same room, in nearly the same positions, and calibrated using the same process. And yet a welcome surprise came in that for me, the improvement for music performance made by the TV2112s was quite strong. Where the Hsus and Monoliths largely sounded great, it was clear even at more moderate volumes that they were subwoofers. With the PSAs, the setup sounds like a fully integrated, true full-range system. There is no perceptible "boom" or "bloat" or "hey there I'm a subwoofer" quality to music anymore. Every bass note appears to be clearly delineated, and this quality holds even with more complex material (multitone). Even at low volumes there is a more nuanced, delicate quality provided by these subs that I had not heard before in any other setup. For me, this was clearly demonstrated by the fact that with virtually other subwoofer system I've used, I would be tempted to create separate presets for music and home theater, with the former configured to run with the subs less hot. I feel no need to do that now, even having since added an additional two TV2112Ms (for a total of four). And yes, I know that this reads like most of the silly audiophile magazine subwoofer reviews you've come across, but these are simply my honest impressions.
So why might this be so? My working theory is that it's a combination of higher motor force and damping factor provided by the PSA's B&C pro audio style drivers that are also more excursion limited than your typical subwoofers with a rolled surround. They might be providing a similar effect to something like a servo-driven Rythmik used in its high-damping setting. I regret that I no longer possess the full suite of REW measurements for the Hsu and Monolith subs. It would be interesting to see what differences manifested in the data beyond frequency response.