Bleach is a classic shonen series, and the lead is Ichigo Kurosaki, who is a fine shonen hero in all the right ways. He was born for greatness, being the son of Isshin Kurosaki/Shiba, a former Soul Reaper, and Masaki Kurosaki, an ex-Quincy, and he soon learned to manifest his powers and realize his vast potential. All this as a human teenager, too.
In the Soul Society arc, Ichigo's greatest rival was Captain Byakuya Kuchiki, the commander of Squad 6 and the head of the noble Kuchiki house. A powerful Captain, Byakuya broke even against Ichigo when they did battle at Sokyoku Hill. If they were to have a rematch and fight to the finish, though, who would win? Going over what each warrior is capable of might help paint a clearer picture.
Ichigo's Powers & Abilities
Ichigo's powers are more diverse than those of most other characters since he has mixed heritage across the board. He was born human, but he had the potential to become a Soul Reaper from his father Isshin and his maximum power can go beyond even a Soul Reaper Captain. What's more, Ichigo also inherited Quincy blood from his mother Masaki, as well as the inner Hollow that came from the White Hollow, a creation of Sosuke Aizen's. Finally, Yhwach's personality manifested in Ichigo as Zangetsu, who took the form of Ichigo's black Zanpakuto.
Ichigo can perform Shikai and Bankai with his Zanpakuto, with the Shikai resembling a cleaver knife and the Bankai (Tensa Zangetsu) having a thin, long blade compressed to maximize its speed and agility in combat. This Zanpakuto is sharp enough to cut through the Hierro armor of an Arrancar, like Harribel or Grimmjow, and Ichigo can perform flash step-like moves while using his Bankai. Ichigo was trained first by Kisuke Urahara, himself an ex-Soul Reaper, then the powerful Yoruichi Shihoin, then the Visoreds, and then his father, in that order. Ichigo has a lot of raw power and sharp instincts that were quickly honed for battle, eventually coming to a point where he was able to stand up to Sosuke Aizen alone. Additionally, Ichigo can fire the Getsuga Tensho, a ranged energy blast whose power scales up with Ichigo's Bankai and Hollow mask.
Indeed, Ichigo's Hollow Mask can push his abilities into overdrive, and he learned from the Visoreds to don it at will. His speed, power and Getsuga Tensho are all augmented and Ichigo can fight without getting tired at all. In extreme emergencies, if he's badly injured or killed and his will is strong enough, he can manifest his inner Vasto Lorde, which had enough power to rival Ulquiorra Schiffer's final form, and overwhelm it.
As a small aside, Ichigo can also perform the Blut Vene technique, hardening his skin with spirit energy to protect himself from harm. This is a Quincy technique that he once used against Yhwach during their first fight.
Byakuya's Bankai & Noble Experience
Byakuya Kuchiki had a much longer, and more conventional, training period than Ichigo, learning from his grandfather Ginrei Kuchiki at the family manor. Byakuya also became a master of the Flash Step, second only to the legendary Goddess of Flash herself, Yoruichi Shihoin. In addition, Byakuya is an expert in kido spells, being able to cast intermediate spells such as Danku and Riku Jokoro without having to use the wordy incantations at all. Riku Jokoro can lock an enemy in place and the Baykurai spell can hit the enemy with a powerful bolt of white lightning.
Byakuya also learned to use Shikai and Bankai and his Zanpkauto, Senbonzakura, is all about combining beauty and elegance with the sharp edge of a blade. Its Shikai scatters its own blade into hundreds of petal-like shards that can swarm around the enemy and shred them, and its Bankai, Senbonzakura Kageyoshi, is the same thing on a much larger scale. In that mode, many thousands of blades form into a massive storm and Byakuya can trap his enemy in an arena of glowing swords with him, called Senkei. Byakuya can focus all of his Zanpakuto's power into offense to destroy his enemies right away, especially with its final form, Shukei: Hakuteiken. It forms a pair of white energy wings on Byakuya's back and grants him a white sword that is the ultimate expression of Senbonzakura's all-or-nothing offensive power.
Ichigo vs. Byakuya: The Rematch
Any fight between Ichigo and Byakuya would be a stubborn, drawn-out match, to say the least. Despite the many years of experience and training, Byakuya has over his opponent, Ichigo has rapidly made up for lost time, enduring intense crash-course training sessions to equal the Soul Reaper Captains. Ichigo will need his Bankai right away to survive Byakuya's Flash Step attacks and Shikai, however, at this point the two would be striking even, giving Byakuya an opening to press his advantage.
Byakuya can use kido spells while Ichigo cannot, and the likes of Byakurai and Riku Jokoro give him an edge. These kido would force Ichigo to don his Hollow Mask, to which Byakuya would respond with Bankai. Ichigo has a slight advantage here -- even if he falls, he could rise again in his Vasto Lorde form and blast Byakuya away. If Ichigo can obliterate Ulquiorra with it, he can do the same to Byakuya, too. Ichigo is the clear winner here.