I don't think Champions of the Just is anywhere near the quality others believe (I found the Fade to be a letdown). And narratively, I think it makes DA:I a great deal worse by essentially neutering Corypheus. In the In Hushed Whispers path, we see a broken and apocalyptic world led to ruin because the Elder One won. We don't need to see Corypheus - we see all of the horror and death he wrought on the world. It's a hokey concept, but at least it makes the Elder One seem to be threatening. And most of all, it features red lyrium - an ever encroaching blight that is devouring the world.
None of that pays off in the quest - but it sure as hell pays off in In Your Heart Shall Burn (one of, IMO, the best sequences Bioware has ever done). After you see a broken world, twisted into an abominable state because the Elder One won, you have the twisted form of Corypheus and his monstrous Red Templars attack you - and they represent the same death and devastation for the world that you saw in the bad future. Without you and the Inquisition, you know that Corypheus wins. Corypheus losing in this case is a reprieve from the build up he's already had.
Contrast that with just a bunch of mundane mages. Instead of Corypheus being threatening, his first introduction is his defeat in In Your Heart Shall Burn. He looks like a chump, because he essential loses with the templars, and then loses once again with the Venatori. You never see the ruin he brings, so there's nowhere near the same desperation to the mid-game quests.
I felt they had differing strengths. In the lead-in and execution, I do think the Mages have the better route- the buildup is a more pressing problem, the faction representative (Fiona) has a better role, and the content of the mission itself really does sell the stakes the best. The world is at stake, because you've seen it after the end, and like you say it gives a good sense of the scale.
Thing is, though? I feel Champions of the Just does better carrying on afterwards.
Inquisition always struggled with what Corypheus was supposed to be. Is he the leader of an army, who can be beaten in the field? Or is he a shadowy, manipulative force, to be fereted out and uncovered like, well, an Inquisition? The mage route presumes the former- the Red Templars as the arch-enemy faction, the gambits for one army after another- but the thing is, you almost never actually need an army of your own to stop him. Most of the time the issue not knowing where Corypheus is in the first place, and there's not a clear use or role for the mages after sealing the breach because, well, what are they supposed to do? They aren't your garrison forces at that point. And they aren't a dedicated military force either. Most of the Mage missions amount to trying to bring in the hiding mages and keep the mages under your banner, rather than doing significant good with them for everyone.
The Templar route plays that better. The Venatori are schemers and conspirators and most of all maleficars. The Templars are used to that- it's practically their job- and they provide the more plausible numbers and networking to expand your anti-Corypheus force to formidable proportions. They've the political ties, the popular support, and the better reputation to feed the Inquisiton's growth. Actual anti-mages to fight the evil mages, rather than... mages to fight the corrupted anti-mages they already lost to, before they went on crack?
Even if we ignore Fiona's previous failings, there's only a one-sided comparison for afterwards. Fiona stays in the tower, does nothing particularly significant, and complains a lot and shows a lack of general self-awareness or improvement upon the Circle, because everything else about the Circle is ultimately at the whims of the Divine. While Barris the Badass goes out, stops demons, protects the innocent, and acts like an ally in hunting down Corypheus, dealing with the consequences of the Breach, and actively helping us stop the maleficar trying to gambit their way to victory through the Dangers of Magic.
Which, of course, the Templars are supposed to oppose in the first place.
So yeah- Hushed Whispers has a better mission on its own terms. But Champions of the Just carries the aftereffects better in terms of the conflicts we have.