Tsunade is an excellent medical ninja, and her healing abilities are exceptional, far better than most. But please don't compare her (even in terms of medical ninjutsu) to Hashirama, who's an absolute legend. He's more of a combatant, yet his healing abilities are superior.
Hashirama's healing (Healing Power) — This ability has the advantage of healing most damage that the user sustains without the need for hand seals. In this regard, Madara Uchiha compares it to
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I don't know if you are aware of the difference but Madara didn't compare Hashirama's healing ability to Tsunade's. He compared Tsunade's healing ability to Hashirama's, and said that it paled in comparison. That's because superior things are never compared to their inferior counterparts, they have a standard of their own. Tsunade's regeneration is great, don't get me wrong. It's just that Hashirama's is better.
Hashirama's healing abilities were unable to regenerate Madara's missing limbs or organs (scan's below) something
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can do.
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Yeah, Tsunade could regenerate an arm, alright. But what makes you think Hashirama's healing abilities weren't capable of regenerating Madara's missing limbs and organs? What solid proof do you have? Did Madara try to regenerate them and failed? Just because Madara didn't use Hashirama's regeneration to recreate his missing limb doesn't mean his regeneration is unable of achieving that feat.
You provided scans trying to prove Hashirama's healing abilities incapable of regenerating Madara's arms by showing that Madara didn't do it. It would be great if you also were able to grasp the reason behind that, from within those scans you provided. Madara implied that he was relying too much on Hashirama's healing powers for everything which made him careless, so he intended on using it less to be more careful. So he was basically trying to prevent the excessive usage of Hashirama's regeneration ability. Plus, Zetsu was there so why bother. Not that he couldn't regenerate his arm using it. He just didn't.
Even if whatever I inferred is incorrect, your argument and reasoning still doesn't make complete sense and is inconclusive. The point is Madara didn't use Hashirama's regeneration ability to recreate his arms. But he could if he wanted. You didn't prove anywhere in you post that he couldn't do that.
Tsunades/Sakura's Healing Powers > Hashirama's
Strongest Healing abilities in the manga!
If you are using this logic to prove Tsunade superior to Hashirama, then I can use the same logic as you to prove Naruto superior to Tsunade and Sakura. Naruto can recreate something as complex as an eye. Tsunade and Sakura can't do that. Hence (using your logic), Naruto regeneration > Tsunade/Sakura's regeneration. And based on that, they are the strongest abilities in the manga. Just saying...