'Sup, Inhuman Here, with something a bit different. This is a fan-theory, and not an actual story. I will be using this theory in my stories when using this specific character, though, until the point in which it is proven wrong. I don't own Bleach, but goddamn, I want to.
As all of you know if you are caught up in Bleach in the manga, the 'Old Man Zangetzu' we all know isn't truly Zangetzu, and is, in fact, the Quincy representation of Ichigo's powers/part of Ywach's soul. And, continuing on that note, we found the previously named 'Hollow Ichigo' is actually Zangetzu. If you are as anxious as I am to find out what Ichigo is capable of now, then you know that all we know for sure at least some of Ichigo's abilities with the 'new' Zangetzu are as follows: the standard Getsuga Tenshou, and the dual bladed Getsuga Juujishou. Now, as Ichigo explained easily quite early into the series, supposedly the Getsuga attack is 'Zangetzu's' special ability, but if one pays special attention, that is incorrect. From what we've seen of Bleach, no two Zanpakto have the same ability, otherwise they would be the same Zanpakto and a paradox will occur, as shown in the 2nd Bleach movie, Diamond Dust Rebellion. Sure, several Zanpakto have had similar abilities, such as Aizen's Kyoka Suigetzu and Shinji's Sakanade both being illusion types, or Rukia's Sode no Shirayuki and Toshiro's Hyorinmaru both being cold types.
However, several Zanpakto have been shown to do the same energy wave attack Ichigo is supposedly signature for. For example, Kokuto from Hell Verse used an eerily similar version of the attack himself against Ichigo. Ginjo used his own green version of the attack with his Fullbring previous to stealing Ichigo's powers. Even Ichigo's father used a Getsuga with his Engetzu in a flashback occurrence, an attack Ichigo stated was specific to himself alone. As other people have theorized, all 'Getzu' or 'Moon' type Zanpakto are able to use the attack, then Aizen would have long since known about it and used such an attack to catch Ichigo off guard in one of their many meetings. Therefore, I believe 'Zangetzu' taught Ichigo such a simple attack under the impression of it being Zangetzu's special ability to prevent Ichigo from finding out the true ability of Zangetzu.
Finally getting to the point of this story, I believe Zangetzu's special ability is just as unique as Ichigo himself: Hollow Abilities. As we've all known, 'Zangetzu' has been suppressing 'Hollow Ichigo', or the real Zangetzu. Since obviously 'Hollow Ichigo' has been referred to as such because he is Ichigo's 'Hollow Powers', I believe that is the special aspect of Zangetzu. Allow me to explain: Hollow Ichigo up until the point of reveal has simply been the Inner Hollow Ichigo has been having trouble with. Ichigo constantly uses the mask Hollow Ichigo allows him to use as a massive power up of sorts in every sense of the word. It increases his strength, his speed, gives him some regeneration, and maximizes his spiritual pressure. Another important thing to notice is 'Zangetzu' is wary of Ichigo using the mask due to its 'hollow nature'. A third piece of information is the most powerful Ichigo has been shown to be without counting the Final Getsuga Tensho, has been his hollow states. In the Ulquiorra battle, that was the turning tide. When Ichigo normally was powerless against the 4th espada, his 'Inner Hollow' or as now known, Zangetzu, took control and used his power to turn Ichigo into a monster, in every sense of the word. It was his most powerful state, and the mask he had after was permanently altered. Seeing as the actual Hollow his mother gave birth to him with has all but disappeared, it is best to assume that as Ichigo's Zanpakto, the 'Hollow Powers' are Zangetzu's specific ability. Unless Hiro Mashima pulls a third bullshit plot twist where the hollow Zangetzu isn't the real Zangetzu, I believe that is Zangetzu's true ability, with Shikai being a simple mask power up and Bankai being the dominating monster Vasto Lorde Ichigo was shown to be in every appearance.
That's all. I now leave with all your minds blown to all hell. King of Insanity out.