[Symmetric] bends have the following advantages. (I) There is less chance of mis-tying an SB, since [b]any asymmetry is [s]actually[/s]--> usually immediately apparent[/b] ... . Moreover, there is more likely to be an easily memorizable method of tying it --often symmetric itself.(II) SBs are usually strong, since neither end is the weaker.
That is, both cords in an SB have the same “strength”, unlike asymmetric bends,
for which inevitably one of the cords is the weaker, and hence the first to rupture
under increasing load or tension. Hence, in general, SBs may be expected to be “stronger”.(III) From an aesthetic point of view, …
On these grounds one might claim that the “best” bends are symmetric.
Roger E. Miles, Symmetric Bends ( How to Join Two Lengths of Cord ), p.3 (Introduction)
Ah, good ol’ REM !
Note the “usually” of his “I” ; I’m not sure I’d concur even
in this, but let’s give that a nod of general favor. (What any
one knot tyer realizes varies individually --and sometimes in
surprising ways (e.g., on this forum, and in another case on
a cavers forum, I recall presumed authorities making mistakes
re the fig.8 of all things!)
Re REM’s “II”, one could as much write “neither side is weaker”,
but that misses the point of weakest link in knotting.
Still, in that I don’t believe that difference in form necessarily
implies a dependable difference in strength (e.g., centuries on
and who knows which is the stronger side/half of the venerable
sheet bend --X1, Knot4U, Roo, … let’s variously test THIS!);
i.p., in one dressing of the asymmetric, butterfly bend, both
sides look to take on good forms; their relative strengths might
vary with material, or possibly loading --and in any case be of
such slight difference as to beg the question of practical relevance.
Also, I think that in some cases (symmetric esp., but otherwise,
too) there can be what computer scientists call “race conditions” :
depending on details of actual loading, one side gets a head start
in tightening on the other (say, identically formed) side (think
blood knot ), and therefore choke(nip)-impedes that SPart
from delivering force to its own choking turn, which enables
the head-start SPart to continue to deliver greater force,
exaggerating the imbalance in loading --maybe one SPart staying
pretty straight & un"deflected" in its tension, the other one
suffering curvature (ah, being “behind the curve” 
) .
As for aesthetics (“III”), beauty’s in the eye of the beholder!
(The “Rule of Thirds” is one of asymmetry.)
