Due to low attack power, which is "compensated" by high speed and defense, Byakuya nearly struggles to keep up with the competition. While having a very high base power Shikai attack, it comes off of his near-paltry 77 base Special Attack stat, which means it will often be more of a liability and a waste of time than a boon. What makes this even worse is that Kido moves, the specialty of Shinigami, are usually special. He also is a very unconventional revenge attacker, being outclassed by even his younger sister, Rukia Kuchiki, due to lack of priority despite Quick Feet and vulnerability to 2nd degree burns, which cut into his decent attack and force him to use his bad special attack. His Bankai form has great defensive stats, but is still lacking offense for a final form.
It's not all bad for Byakuya, though, seeing as he has relatively high defensive stats at 99/113/117, which ensure that he is not OHKOed by anything and not 2HKOed by most attacks. His Bankai is still amongst the most powerful of all of Soul Society, being able to hit multiple opponents with base power attacks of over 300. Altogether, these factors still don't keep Byakuya from struggling with top-tier attackers, but it does give him a moderate fear factor and a relatively high competency rate.