I love the term "musical" when used to describe audio gear!
Musical? What is that anyways. I mean, musical as in after you eat a can of beans kind of musical?
I think a loudspeakers' characteristics are degrees of:
a) dynamics
b) control
c) relative smoothness
d) range
e) output
Best terms used to describe a loudspeaker are on the scale of either realistic or natural. After all, reality is what sound systems are trying to reproduce (something real which was recorded).
There are tonnes of subwoofers available out there, some will be more realistic & natural sounding in reproduction than others. I have heard a few but not too many. It seems most of them are super inefficient but handle large amounts of power, occupy small footprints and employ massive cones (Kind of like driving a garbage can lid in place of a cone). In other words, they have the range and output but sacrifice dynamics and smoothness.
The most natural & realistic sounding subwoofers will use a high Q driver in a large enclosure. Nothing sounds better than that, in a subwoofer or otherwise. Ideally, in a powered subwoofer, you'd want an amplifier that was built specifically for the driver in a specific enclosure. You could build your own passive subwoofer too. I've yet to get around to it but I'm going to do just that using a single 18" custom made driver. It should (I hope) sound really natural and not break the bank.