What base 12 gives you is a lot of common divisors: 2, 3, 4, and 6. Base 10 only has 2 and 5. Base 16 only has 2, 4, 8.
The practical upshot of this is that you can divide things evenly in more ways. Particularly when wanting to divide a board into thirds. Having 12 inches to a foot is actually helpful there, though it falls apart as soon as you get larger.