With the mage you get a couple extra dialogues (I might miss some)
- Perseverance
- First Kiss
- Lake date
- Abomination talk
With the Templar you get a lot of extra dialogue just going with the class that isn't romance-related, but if you are in a romance, it takes on a whole new level (moreso if he is also taking lyrium):
- When Cullen first tells the IQ that he stopped taking lyrium
- Perseverance
- Prayer Scene
- Pre-Spec talk
- Post-Spec talk
- Post main campaign talk (haven't gotten there yet, but have heard about it)
I'm not sure if there are any changes during Before the Dawn. I will have to let you know on that.
I understand how some like the mage dynamic, I just don't. Most of the extra content is the IQ questioning him over and over..."I'm a mage, is that ok???" "You're alone with a mage, is that ok???" When I played through as a mage it actually started to wear on me like a girl constantly asking her b/f if he still thinks she's pretty. With a Templar, yes there's more angst, but to me it feels like they're challenging each other as equals, rather than the mage always needing confirmation of his feelings. I guess it's just a self-confidence thing? I dunno, that's just how I see it. Folks are free to play the game however they wish. That's just my take on it! 
I actually want to go thru as a Templar and try the romance (I have been watching your videos)! The mage stuff does get a bot needy at times, i agree.
But I was actually referring to siding with mages (not being a mage, per se) and getting the extra quest with Cullen (i.e., rather than Leliana)...thus it feels like you get more romance with Cullen in that regards, in comparison to Solas and some of the others. I am spoiled for all that extra content, which would make romancing Solas hard for me personally, even though I do like him...
Edited - cause i see this was already discussed in my absence!
Gah, i am out of it today! Migraines are the worst 