“Why choose a viola bass instead of a P-Bass”…
I'll ask you another question: “Why choose a P-Bass instead of a Jazz-Bass?”
The J sound is more brilliant, as the P is more warm.
With the viola, it is exactly the same kind of answer: the details of the sound.
The viola produces a rich, warm, medium bass, without the shiny sound of the J bass.
It could be even warmer (and less brilliant) with round wound. Not exitinct, simply less brilliant.
Medium global sound is something hard to get with a P-Bass, because it quickly becames slimy. But with the help of the hollow body, the viola produces a really nice and balanced medium sound. The passive design and the floating bridge makes it difficult to adjust an tune, with no help from the strange pots design.
Clearly, it is not a funky nor motown bass. But it could sound great, with rich and profund lows, mellow mediums, and a really nice-but-not-aggressive attack.
But with a little fine-tuning of the humbuckers and rewiring of the pots, you could make an easy to carry versatile bass, with a clear 70ies vintage sound.