"Dynamics" is a good word to describe the variety and responsiveness of an Alembic circuit. They allow for so much more nuance in your playing, and for me, that is a significant factor in creating music with its own dynamics.
I know exactly what you mean about taking a P Bass to a gig as well as an Alembic, and favoring the Alembic for the night. You know immediately that the tone and presence is lacking when using the Fender, and everything comes back into focus when you plug in the Alembic. There have been very few gigs where I could use the Fender all the way through. If the music is varied, and other than blues or classic rock, the Fender just won't hang. If you have to sound more contemporary, or have a slap solo, the Fender does not have the clarity to pull it off, or at least, not in a way that is pleasing to my ears or the audience's. Using the Alembic will give you all the tones you want, from vintage Fender to just about anything else, while still maintaining clarity in the mix. On top of that, you still get the pure Alembic tone which is something no other bass can match.
As to "finding the nuances", you can save yourself frustration by understanding how the Q system in an Alembic works. Once you recognize it works more like the dials on an EQ unit, you will be able to choose your boosted or cut frequencies easily, and thus make sense of how to achieve the tone you are looking for. For me, I find that leaving everything all the way up with the Q switches off is a great tone. If I need the sound to cut through a bit more due to odd acoustics in a particular venue, I will turn the Q switches on so I get more of a single coil sound. For my fretless Alembics, I will use mostly the bridge pickup, and turn on the Q switch with the tone knob about 2/3 down to boost the low mids. That gives a great Jaco tone.