Question: I was wondering if there was a reason that the Fire boon Blazing Weapon seemed, well, measurably worse than the Frost boon Hrimmthurssar's Touch. The Frost power costs 1 Legend and 1 Willpower for the whole scene, and automatically adds additional damage dice equal to the number of Frost boons to BOTH unarmed and melee attacks. And there's an alternate use.
Indeed, there is a reason! The two boons are not intended to be identical, and their different capabilities naturally lead to different mechanical implementation.
Hrimmthurssar's Touch does have advantages over Blazing Weapon, at least in terms of dealing damage; it can be applied to both weapon and unarmed attacks as the Scion wishes, and it automatically grants damage dice equal to her Frost boons. It also has the ability to freeze water and other vulnerable substances with a touch, which is helpful when you really need to cater that divine party and just don't have time to call out for a few bags of ice.
Blazing Weapon, on the other hand, can get up to a Scion's Fire boons in dice, but may also get fewer if he happens to be catastrophically bad at the boon's Manipulation + Occult roll. It can only grant those dice to weapon attacks, not unarmed ones, and doesn't have the additional party trick that Hrimmthurssar's Touch is rocking. However, Blazing Weapon also has the ability to grant its bonuses to the Scion's allies, lighting as many weapons on fire as the Scion wishes, and further it can create weapons out of nothing if an unarmed Scion needs them, two things Hrimmthurssar's Touch can't do.
Basically, Blazing Weapon has slightly less potential for overall damage because it's more flexible than Hrimmthurssar's Touch. It uses a roll instead of a flat value because its successes can be apportioned between various different things - damage on weapons, yes, but also accuracy and defense on a new weapon that is created by it and multiple weapons that can be lit on fire at the same time. It's also higher-level than Hrimmthurssar's Touch because it has a much greater damage potential once a Scion gets to Legend 8 and can pair it with Baelfyr, making its damage aggravated (which is something the Frost purview can't duplicate, even at that higher level). It's also worth noticing (if only a minor issue) that there are only 17 boons in the Frost purview as opposed to 21 in the Fire purview, which means that Hrimmthurssar's Touch will always have a slightly lower damage cap than does Blazing Weapon.
In fact, the only things Hrimmthurssar's Touch has over Blazing Weapon are the slightly reduced cost (depending on your point of view - for some characters, Willpower's at more of a premium than others), the inability to roll low and the ability to roll Brawl instead of Melee for attacks. In every other way, Blazing Weapon's superior and furthermore can gain in power as the Scion grows in ways that Hrimmthurssar's Touch can't, so we're comfortable with the first being higher-level and more expensive than the second.