Are you talking purely about game mechanics, or the characters in the story? If the latter, a Seeker should be able to shut down any mage, with sufficient preparation, and with other Templars to help. As I understand it, Templars overwhelm a single mage with force of numbers and a lot of lyrium.
But Trespasser Solas isn't any mage. He's part Evanuris too. So who knows? He's still mortal, as far as we know, and just one Knockout Bomb would probably be enough to take him out. Even a strong cup of tea might work.

For game mechanics, Rift Mage would win every time. Every Veilstrike and PotA hurts the Templar's DPS, since they essentially can't do anything for those durations. Stonefist with the stagger upgrade can come pretty close to stagger locking a Templar. And if the Rift Mage has the Ring of Doubt, forget about it, since the Templar has to close to melee range to do damage. Even Fade Step is going to make any melee difficult.
Swap Blackwall for Cass and I think it's a more even match. Any kind of anti-stagger/knockdown buff would minimize the Veilstrike/PotA advantage. Champion has those abilities, so would probably have higher effective DPS. Still going to be difficult with Ring of Doubt, though, and Rift Mage being able to attack at range.
The one ace up the sleeve of a warrior is Grappling Chain/Give Them The Boot. If a warrior can land one of those while the mage is not invisible, they can get in some high damage hits before the mage recovers. Grappling Chain, then Wrath of Heaven, then Spell Purge might be enough for Cass to take Solas out, though it would take 3 or 4 iterations.