The Sundered weren't equipped to handle the Final Days better than the Ancients, the story is simply written to always disallow the protagonists to actually stand to lose anything of note no matter what threat they are dealing with at any given time.

Much like how, despite the Warrior of Light travelling to the First, conveniently none of his enemies made a move to successfully sow chaos and destruction back on the Source.

The Final Days also only emerged in certain places in both the Unsundered and Sundered world. It was a gradual process. That it only emerged in a handful of regions on that basis has nothing to do with the Sundered being 'better equipped'. Zodiark was also keeping the Final Days at bay up until his defeat - which isn't anything tied to the Sundered, themselves.