I find both of these necklaces interesting to look at, largely because the lack of symmetry continually draws my eye and my brain.
I prefer the second to the first because your own instincts partially betrayed you. Despite throwing out your self-imposed symmetry rules, I still see an echo of symmetry--particularly in this second piece--that employs color and shape matching on complementary sides (a vertical symmetry) even though the particular beads aren't truly identical. :D
Upon closer inspection, I find that the first necklace also preserves a little symmetry, at least in a balance of approximate sizes and shapes along a vertical, left-right symmetry axis.
I find that rather cool... ;)
P.S. I so look forward to life in the New Heavens and New Earth, because we will have ultimate liberty to work and create without the pressures of having to scramble to provide for our own survival.
Some symmetry is inescapable in making it functional and the manner I constructed it. I made several similar beaded wire segments using similar varieties of beads to achieve similar lengths. I also deliberately chose the two pieces with the largest beads as the center of the pattern. After that, I just grabbed from my pile of premade segments.
The apparent order in the second was an accident of not wanting the same colors adjacent, leading to a sort of symmetry in splitting them apart.