Finally, Shrivelling has more competition for offensive options on new investigators. Azure Flame matches Shrivelling in a lot of ways - It's a 3-Cost, 4-Charge Spell which uses Willpower and deals +1 damage. Shrivelling remains a mainstay in Mystic decks for a reason, and that identical core functionality means this can compete with it. The only question is, how does it stack up?
The immediately notable difference is the downside - while Shriveling hits your sanity on , , , , or , Azure Flame instead hits your health on +1, 0, or . How does that compare?
In terms of how often you hit the downside, Azure Flame comes out ahead. At first, on Normal difficulty, it looks relatively even - there tends to be a 1 token difference between the two, one way or another. However, most campaigns will muck around with the bag, and do so by adding negative tokens - tokens that always add to Shrivelling's set. This means that over a normal campaign, you will tend to hit Azure Flame less and less, and Shrivelling more and more. That's also discounting the fact that Azure Flame becomes even less problematic at harder difficulties, where +1s and 0s fade and negative tokens increase.
This also impacts its synergies to some degree. It's the middle-of-the-road option if you're messing with token effects. Dark Prophecy won't help like with Wither, but neither will it hurt like with Shrivelling. Eldritch Inspiration won't be of any use at all, and Counterspell and Defiance can only be used in their more general 'prevent a modifier' effects. There's a small amount of synergy available with the unusual seals (Shards of the Void if you're running both, Crystalline Elder Sign, and The Codex of Ages for Father Mateo). These are worth keeping an eye on if you're low on slots and need to pick between one and the other.
The other main question is if you can deal with the downside when it hits. Shrivelling hits for horror, which Mystics tend to have a higher tolerance for, and which they and may have more measures for. With Holy Rosary, Arcane Initiate and Fearless as common picks, sanity damage is something Mystics can usually take. On the flip side, regular damage is harder to mitigate, with David Renfield as the only Mystic ally with more than one.
The final item for comparison is a deck-building consideration, and will depend on what else is available when Azure Flame is eventually released. One major part of a Mystic's consideration is Arcane Research, and the bonus XP it can provide. Shrivelling has a large opportunity for upgrades, allowing you to go to Shrivelling (3) or Shrivelling (5) over two different sessions. Until we find out if Azure Flame has upgrade options, it will not be able to take that XP, which may result in some waste over a campaign.
To summarize: If you have more health to spare and are trying to pull the classic token modifiers, Azure Flame probably wins. If you have the horror to spare, are already trying to avoid the classic token modifiers, or are using Arcane Research, Shrivelling takes it.
Of course, if you're looking to have consistency with your attack spells, there's also a good chance that you'll just want to run both. Azure Flame's consistency is comparable enough to Shrivelling that it may take the place of Wither for any mages who simply needed one more attack option.