The design of the two classes is very different, making comparisons in a vacuum like that is worthless.
N.AST has a better healing power than SCH when it comes to sustained healing and MP management. SCH can't afford to top its party after every mitigated mechanic as using Emergency Tactics+Succor is a huge mana loss. You could use Indom, but that cuts you from any instant group healing and uses a flow stack... and it won't be available everytime. Using a Helios after a mechanic is way more affordable.

The intended way to deal with stuff as a SCH is to mitigate as much as possible through the use of its huge cooldown toolkit, and then letting the WHM deal with the post-mechanic damage (or poping Whispering Dawn for good measure) while going in Cleric to get back DPSing.
N.AST's toolkit is much more reduced, but post-mechanic heal being both powerful and affordable makes up for the increased damage the party would take. It also ease the WHM's job where Medica+Helios would do the job instead of a situational Cure III. I'm pretty sure that the WHM would be able to DPS way more with a N.AST than with a SCH due to simply sharing the party-heal duty. It does require extremely good coordination tho'.

Mitigating or healing damage share the same goal, so, as long as you can leave your party above 0HP after a mechanic, it doesn't really matter what you do to achieve that.
The issue with N.AST is that its sustained DPS wasn't good enough to make the cut compared to a SCH, but the way they both maintain their party alive was fine. So, now, with buffs to the cards, this DPS issue might get more or less solved, and the buffs to shields will allow for more overall mitigation, ensuring that it's enough for probably every upcoming mechanic.