Best sub for music,

Don’t overlook Rythmik.  These are very good sounding and well made powered subs for music.
https://www.rythmikaudio.com/F12SE.html

I do not know where this differentiation between home theater subwoofers and HiFi subwoofers came from. There are good subwoofers and bad subwoofers. Perhaps home theater people tend to buy bad subwoofers. Good subwoofers will do anything. They are even better at doing theater than bad subwoofers. 

Most commercial subwoofers are not even fit for home theater duty. It is very hard to make an enclosure that works at a reasonable price not to mention terrible cross over strategies. Play anything with a lot of bass and put your hand on your subwoofer. That vibration and shaking is distortion. Ideally you should be able to put your hand on it and feel absolutely nothing. I made 200 lb enclosures out of solid surface material and I could still feel some vibration. Next versions will be better.
Stay away from ported subwoofers. Subwoofers have to move a lot of air and it is very hard to avoid port noise. It is better to stick with sealed designs and correct the frequency response with power and room control.
The best subwoofers now use what is called a balanced force design. Two identical drivers are placed at opposite ends of the enclosure and operate in phase so the vibrational forces cancel out.
 Regardless of the size of the room the minimum size is two 12" drivers or four 10" drivers. Bigger and more is always better. The less work any single driver has to do the lower will be the distortion. Making sub bass requires long excursions which take the suspension out of it's linear operating range. Bigger and multiple drivers do not have to move as far. The thought that smaller drivers are "faster" is beyond silly, another example of lay instinct run amok. The sign of a driver not being "fast enough" is it's high frequency response falling off. Any subwoofer driver that can make it to 500 Hz is more than fast enough. I do not know of a subwoofer driver that can't make it to 500 Hz. There are lots of great drivers out there. It is the enclosures that are the main problem followed by poor integration strategies and crossovers. Digital bass management and room control are essential to achieve the best results. 

The best sub for music isn’t a sub but a bass extension. Genelec W371a with GLM digital management. Bargain at $19K a pair.

https://www.genelec.com/w371a

   A sub's material of construction? While important in the basic sense of what manufacturer wants to use in their products, does not address your question.."Best Sub For Music".
   Don't obsess about materials of construction. Think about how you want music to sound. Sub integration can be a most challenging task and experimentation is most often needed to achieve the results YOU want. Millercarbon made a brief but important statement.
   I have gone thru some length of time to integrate my subs to deliver the sound I prefer. If you're serious about how to really get sub performance to compliment your music I would refer you to this article. It's one of the best I've read on the subject. It's quite lengthy but if you are patient and want to know how subs work read.

http://www.soundoctor.com/whitepapers/subs.htm

A good sub for music is one that can handle whatever HT throws at it.

If it can't handle cinematic effects it's never going to be able to cope with all types of music.