These types of fanboy showdowns always amuse me. In the red corner, Cosmoe, who spends every waking moment raising the alarm about the underusage and underpowered-ness of his pet DG! In the blue corner, Celmare, who bristles at the very notion that QoT is relatively weak!
My $.02: QoT is relatively weak, but not because of Bramble Shield. She's squishy, slow, her spells cost too much mana, and to top it all off her AA stinks. Also compared to Sedna she has no interrupts, no reduced-cooldown aura, and no super-priests.
As for the direct Heal vs Shield comparison: I'm a bit surprised to see so many posters on the pro-shield side of the debate. Shield is slightly better early on, but above level 7 (Heal 3+4 vs Sheild 3+4), Heal is 2,384,951 times better because it purges negative effects. Yes, its that important.
QoT could do with a buff.
This man is correct.
For the support role, Sedna is plainly better than QoT.
For the "shielding your whole team before a battle" argument, don't forget that shields are only useful if a shielded demigod actually gets attacked. In other words, it is often a waste of mana to shield allies out of combat, only for it to expire, having absorbed 0 damage.
On that note, shields are also rarely worth their full mana cost, because they often expire before they collapse from damage! Heals, on the other hand, are ALWAYS worth their cost, so long as they're not used on a full-heath or near-full-health ally. Plus, you get more health-per-mana with heal than shield, AND shields have no armor! The net effect is that you will be seeing much, MUCH higher mana efficiency with heals than with shields.
As someone who has played both QoT and Sedna extensively on a premade team, I can say there is no reason to use QoT over Sedna. Sedna is faster, tougher, has better support abilities, has MUCH better survivablity, doesn't have to deal with form-changing (which, by the way, is an added hassile for QoT and does not net her any rewards for her trouble), and on top of it all, Sedna has a powerful attack with an interrupt!
Seriously, folks. Until QoT gets a huge buff, start playing as Sedna. You won't regret it.