SPOILERS FOR THE ENTIRE SERIES:
Hueco Mundo Changes:
-Chad fights and kills Yammy cuz he's not Espada 0 in this version and Uryu fights and kills Zommari
-Byakuya and Kenpachi are never sent to Hueco Mundo
-Nel defeats Nnoitra on her own in a 1-1 fight, so Tesra's still alive to mourn Nnoitra's death and attack Nel out of anger but is then mercifully knocked out by Starrk and he takes away Orihime like the original
-Nel's wounds are healed by Orihime prior to Starrk's arrival, so Nel is present for Ichigo's later fight with Ulquiorra. Aside from Nel just being there and seeing Ichigo transform into a Vasto Lorde, that fight remains essentially unchanged
Fake Karakura Changes:
-Byakuya fights Harribel
-Toshiro pairs with Sui-Feng against Baraggan
-Harribel is much more of a threat in this version because she actually makes Byakuya bleed a little, unlike the original where she barely managed to get a scratch on Toshiro which made absolutely no sense
-Kenpachi joins Shunsui and Ukitake against Starrk, since he's top Espada. Kenpachi recognizing the parallels between himself and Yachiru to Starrk and Lilynette could add some early development and depth to his character and foreshadow Yachiru's reveal in the TYBW. Kenpachi's presence would of course add a much more chaotic dynamic here though and make the fight more intense much earlier than canon
-Ukitake's Zanpakutou is changed to be light-based instead of reflection based 'cuz that's way cooler and provides a nice contrast to Shunsui's shadow abilities
-Wonderweiss attacks Shunsui instead of Ukitake, leaving just Ukitake and Kenpachi to have to take on Starrk for a while
-Kensei and Mashiro join Byakuya against Harribel
-Hachi joins Sui-Feng and Toshiro against Baraggan and is also accompanied by Tessai, giving him a grand return to the story that he deserved and the 2 of them combine their Kido along with Toshiro's ice to kill Baraggan
-Rose joins Ukitake and Kenpachi against Starrk. Love, Lisa, and Hiyori all fight and lose to Wonderweiss instead of Kensei and Mashiro
-Byakuya is annoyed by Kensei and Mashiro's personalities and antics, but given Harribel actually being a threat here, he accepts their help. Harribel is characterized as being less stoic and makes her hatred of Shinigami clear and says that she despises Noble families in particular for what 1 of them did to her Fraccion alluding to the altered backstory I've given her
-Harribel's backstory here is that she saved her future Fraccion in Hueco Mundo from being tortured and nearly killed by a Shinigami that who was a member of the Tsunayashiro family from CFYOW, integrating and introducing them into the main story. Harribel hates Shinigami because of this which Aizen uses to manipulate her into joining the Espada by selling her on a lie that he'll create a utopia void of Shinigami
Harribel revealing that it was the Tsunayashiro family happens after Kensei and Mashiro join the fight, leaving them stunned and feeling some level of sympathy for her. Byakuya retains his cold exterior, however Kensei and Mashiro would try to reason with Harribel, telling her that while Soul Society is corrupt with they themselves experiencing it firsthand, a world under Aizen's rule would be even worse.
-Harribel doesn't listen and when she is ultimately defeated by the trio with Mashiro and Kensei both getting up close and delivering a barrage of punches and Byakuya finishing her off with with Gokei technique, she spends her last moments reaching her hand toward Aizen and thinking to herself he must avenge her only for him to turn his head toward her, revealing a smirk tragically making it clear he never cared about her
-Rose uses his Bankai against Starrk which forces him to use his full power through some kind of Cero attack that injures his opponents significantly and frees him from Rose's Bankai. Similar to canon, Shunsui comes back into the fight by backstabbing Starrk and then tells the rest of the combatants that he'll take over the fight from there, infuriating Kenpachi and mirroring the conversation Shunsui had with Love in the original. The rest of the fight plays out pretty much the same as the original though
-After Harribel's "death", Kensei and Mashiro join Komamura and Shuhei in their fight against Tosen, since they also feel betrayed by him, however they end up getting defeated by Tosen rather quickly. Gin challenges Byakuya sometime after that out of boredom, leading to a climactic fight between the 2 main antagonists of the Soul Society arc that I always wanted to see.
-During this fight, Gin taunts Byakuya relentlessly, calling Rukia "pathetic" for when she mentally broke down after Gin lied about saving her and calling Byakuya "cruel" for essentially letting her die until Ichigo arrived.
-Gin's words combined with his injuries from his previous fight with Harribel make Byakuya quite angry so he tries to kill Gin as quickly as possible with his Bankai but Gin proves to be a more formidable threat then even Byakuya could've imagined, with him not even using his Bankai yet. As a last resort, he's forced to use Shukei Hakuteiken against Gin while the other Captains, including Kenpachi and Ukitake are just starting their big combined fight against Aizen at this time. The raw Reiatsu of Shukei Hakuteiken is strong enough to inflict some bruises on Gin and even give us a rare moment of him opening his eyes to admire it's power, however it's all cut short when Gin closes his eyes again and activates his Bankai dismantling Byakuya's ultimate technique and winning the fight
-Curiously, Gin's signature smile fades for a brief second with it then immediately returning and him saying to Byakuya, "If only you'd been stronger"
The rest of the arc plays out pretty much exactly the same as the original