1) which tank requires less healing 2) which tank takes less damage overall.
For all intents and purposes, those 2 questions are functionally asking the same thing (which tank requires the least healing over the course of a fight), though there is a bit of a semantic differentiation. To answer them explicitly, Shadows require the least healing but take the most damage overall while Guardians simply take the least damage. The reason that Shadows take the most damage but require the least healing is because they pack a goodly portion of consistent self healing; without it factored in, they have the lowest mitigation, but, with it, they have the best (which means that the least amount of damage gets through to them that needs to be healed by outside sources). Guardians get around this by having an absorb barrier that simply prevents them from taking damage, though it operates in much the same way. In addition, Shadows also have the best CDs (as described by survivability contribution normalized by uptime), so, if they use them properly, they'll take even less damage compared to the other tanks.
It's also important to remember that "damage that needs to be healed" isn't the only important metric by which to gauge a tank, especially since the non-CD mitigation of each tank is within a 1% margin of error (Shadows push something like 77% mitigation w/ their self heals factored in, Guardians 76% with Blade Barrier, and VGs 75%). The other side of the coin is in the predictability of needed heals, i.e. how "bouncy" the hp pool tends to be. VGs have the most stable hp pool, thanks almost entirely to the fact that they have the highest K/E DR by a significant factor. No attack gets around DR and a vast majority of incoming damage is K/E, so, in pretty much every fight you're gonna see, VGs are going to have a more stable incoming damage profile. Guardians are marginally worse, thanks to their lower K/E DR, and Shadows have it outright worst. Guardians and Shadows, of course, make up for their lower K/E DR by having significantly higher Defense Chance, which means that, just as they're likely to get a string of hits that unluckily penetrates their mitigation chances, they're also just as likely to get a string of hits that gets completely ignored thanks to their high mitigation chances. It's a give and take, but it also means that they're less predictable overall.