Hardened Elegance
While I understand that appearance should not be a huge factor in character analysis, I do find Byakuya's design to be particularly well-crafted and meaningful. A character's image subliminally communicates messages about them, so in Sherlock Holmes fashion, let's look at what we can observe about Byakuya through his physical features.
A Pretty, but Brooding Face
Though he first appears a bit gremlin-like, Kubo does refine Byakuya's polished, regal beauty to a caliber befitting his elevated status. Many female shinigami are reportedly infatuated with him for this reason, perhaps further encouraged by his mysterious, cold demeanor.
Speaking of which, Byakuya's mouth is either set in a straight line or a frown--even in promotional illustrations. He seems constantly burdened with private thoughts no one else will know, an image amplified by the distance often present in his eyes. It's a welcome contrast to the louder character designs that color much of the series.
Flowing Gait, Severe Carriage
While Byakuya's relatively broad physicality makes him seem grounded, there is also a graceful, airy quality to the way he moves. The length of his hair plays off this very nicely and enhances his elegance as it flows around his face. It also helps that he makes everything look effortless, including disappearing from sight even after sustaining grave injuries.
The combination of grace and austerity in how he carries himself befits his status as both a captain and a noble, but it does project a paradoxically unsettled serenity. His body moves as if he were air itself, and his prideful demeanor suggests an uncompromising ego. And yet he is not at all free-spirited, instead weighed down by his sense of duty and a calculating mind.
Sharp Silhouette
From his sculpted chin to the tips of his layered hair, Kubo made Byakuya's features as sharp as his arrogant remarks--and carefully so. Characters with smoother contours are generally more agreeable (i.e. Ukitake and Unohana), while "spikier" characters (i.e. Ichigo and Renji) appear more unkempt and wild. I guess the best metaphor I can think of for this is a thorny rose; that is, Byakuya has the ingredients for a delicate character, but he's got enough bite to him that you wouldn't want to get too close.
In his updated character design, Byakuya's layered hairstyle flows closer to his person and in rounder waves. It seems less severe and also emanates a more mature self-assurance, perhaps a positive result of his experiences in those interim months.