I just started up Fates. It sounds like the color triangle in Heroes is not just a simplification of the parallel weapon and magic triangles from the other games, and is instead just the system that Fates uses? Although in the main games it's mostly affected accuracy rather than damage.
I'm not sure I like the idea, in Fates or Heroes, but especially in Heroes where it has a huge impact on (expected) damage. It's just sort of random that my Pegasus Knight is going to be very vulnerable to one particular kind of magic, and interferes with its role as a mage-hunter. And suddenly my mage can actually tank an attack from a high-damage melee class, as long as they're using the right kind of weapon.
And in Heroes they've cranked up the impact of triangle advantage significantly. In the main games it's typically been something like +/- 15 Acc and 1 damage, though in Fates it's apparently 20 and 2 for the highest weapon rank. The damage boost is not that significant at end-game and the accuracy is probably not a huge change in your expected damage. Either it's a ~20% change in expected damage for a high-accuracy character or it's a low absolute change in expected damage from a low-accuracy character. In Heroes the 20% buff applies to Atk before Def is subtracted, so is often a huge multiplier increasing expected damage by ~10.