Both paths clearly have their fans. Personally I perfer Hushed Whisper (in spite of the cliched time magic angle). What's more, Hushed Whispers makes more thematic sense (at least to me) and I'd be very suprised if that path didn't eventually wind up being the default and/or canonical path.
Why? When you go to Val Royaleux for the first time, you get no indication that you'll have any opening at all with the Templars. In fact (what you think is) the Lord Seeker treats you with the grace and politeness due to a gnat. You get the idea (if you listen to Cassandra) that there is something terribly wrong with this, but it doesn't scream EMERGENCY nor do you really seem to have a good wedge for a negationation to close the breech.
OTOH, just as you leave the Grand Enchanter, herself, at great personal risk (Solas will mention this) gives you a personal invitation to Redcliff to at least discuss how to close the breech and how the rebel magi might help with this. She goes out of her way to be inviting and gracious (quite unlike the Lord Seeker).
Given the two options, I think that a fair minded person would logically go to Redcliff next since that's the obvious opening and at least see what terms the rebel mages are looking for (with the idea that if they are too onerous, you approach the Templars instead). Once you get to Redcliff and find out that a hostile Tevinter magister with universe threatening magic is now not only controlling the rebel mages but also has effective control of Redcliff, this IS a bona-fide EMERGENCY and I don't see how a reasonable person doesn't make that a priority at that point.