Most other answer focuses on how to 'buff' slow magic and 'debuff/nerf' fast magic. Here my answer will try to answer how slow magic can still be competitive in a world that have fast magic.
Here is my assumptions:
- this answer only covers (exclusively) how magic is used in combat (so it will not cover pre-prepared magic weapon, using magic to increase economic output, how it's perceived by society, etc.)
- the combat/battle is assumed symmetrical (organized army vs organized army, or individual vs individual, criminal gang vs criminal gang, or paramilitary vs paramilitary), so slow magic IS NOT MORE ORGANIZED than fast magic (assume same number of personnel and same organization style)
- magic is realized (actuated/actioned by) gods, here I assume there are multiple gods:
- some are more powerful than the others
- some are stupid, some are smart, some can read your intention well, and some can't read the room (e.g.: KY)
- some are personal (have personality), some are not personal (just a deus-ex-machina in its literal meaning: a machine that is very powerful and transcendent, but it's just a machine, does not have will)
- some like a certain behavior, some don't (think of yourself: you like people who is dressed nicely/neatly, and you don't like someone who smells like rotting corpse)
- both slow and fast magic have almost everything the same:
- same range (number of km or mile to its target),
- same firepower (how many joule the energy it can project),
- same timing (can be commanded to be triggered on impact, or on delay, or on proximity, etc.),
- same flexibility/mobility (a homing spell from both slow and fast mage have same turning radius, same acceleration/deceleration)
- what is different however, is that slow magic is slow, and fast magic is fast (duh).
- slow magic needs "ritual" (action done by person/people) and "ingredients" (materials/tools/consumables that is needed to perform the magic)
- fast magic only need chants/spells: it can be spoken quickly (think of how most magic in fictions, the mage shout "fireball" and from the end of his/her staff a fireball flies to its target)
Intuitively, it may looks like fast magic is always better in every sense. But no, it's not. We only think of it that way because we think that the "ritual"/"ingredients" are just wasted efforts that some arbitrary "gods"/"elders"/etc. forced on us. We think that way because we're in modern society that has outgrown such practices.
So here's the reason: Assuming that magic is "a way to alter reality", then "spell" (for fast magic) and "ritual"/"ingredients" (for slow magic) are actually a way to transmit information to the gods/forces/world on what reality needs to be altered, how it should be altered, what is the expected end result, who should alter it, etc. (think of 5W 1H question).
Example of combat "spells" (fast magic):
- "shot fireball from the end of my wand!"
- "shot thunderbolt from the end of my wand!"
- "shot pebble from the end of my wand!"
- "shot water jet from the end of my wand!"
- "increase my muscle strength!"
- "block incoming projectile that is approaching me!"
Remember here that the scope of this answer is only application of magic inside combat (so spells like "give me thousand gold coins!" is out of scope)
Example of combat "rituals" (slow magic):
- prepare X amount of lizard eye, each pointing at different direction (meaning: longitude, latitude / coordinate of the target to strike is encoded in the direction of the eye), draw a lot of circle with smaller circle surrounding it (meaning: the payload/warhead is TNT, it's encoded in what kind of circle is drawn, in this case the circles are actually the chemical symbol of TNT), write number 3928.245275 in your staff then point your staff at the sky (meaning: drop it from the sky from altitude 3928.245275 meter/mile/whatever unit of measurement your world have), write the name of the god and draw his/her icon/coat of arms/callsign/etc. you ask to execute the magic on edge of the ritual space (meaning: this request for magic is directed to this god only)
By this point anyone would have realized that by doing "rituals" (slow), the amount of information that can be used as "parameter" of your magic strike is increased dramatically instead of using "spells" (fast). Also, calculating those parameters require writing equation/doing math on paper/parchment/floor/etc. that is by untrained eyes looks like just another arbitrary ritual (its not, its required to do a precise targeting).
This means fast magic CANNOT do precise reality altering magic and is limited to approximated reality altering magic. Command to "shoot fireball from the edge of your wand" is a very approximate (unprecise). The fireball can be big, small, fast moving, slow moving, homing, split to multiple, or any other variation depending on which god is present in the place to execute the magic. But it's not making fast magic unusable: in the heat of battle, whether the fireball you shoot is fast/slow/small/big/etc. is a small concern, your direct concern is to disable the enemy in front of you (you do not need to understand/think about implementation detail)
But in case of slow magic, all the parameters you send before executing it is very important. You can designate coordinate, altitude, firepower, trigger (time based/impact/proximity), special behavior (homing, non-linear movement speed following a polynomial equation, how to cancel/defuse the magic, etc.). Doing the same with fast magic is POSSIBLE, but NOT FEASIBLE in the middle of heated battle (who in their right mind would do algebra/recall chemical compound symbol/measuring distance while dodging arrows/bullets/swords? even if you're a genius, the speed of your vocal cord is still the same as normal humans, so speaking a very long and detailed magic command in the heat of battle is not a good idea, you should just speak faster and more crude/approximate command with more "command per minute" instead).
Also, fast magic is not very consistent/reproducible: same spell can be interpreted by different gods that interpret it differently, or if a parameter is not specified, the gods fill it with whatever value they like). So another advantage of slow magic is consistency/reproducibility.
This would make interesting worldbuilding since fast magic practitioners would be more of hunter/warrior type while slow magic practitioners would be more of scholar/mathematician/scientist type. Also, slow magic practitioners would tend to only call on some specific gods (only smart, precise, calculating, consistent, deterministic) gods, which would make them only able to perform their rituals from specific places only (where those gods that they prefer dwell); while fast magic practitioners can fight anywhere, utilizing whoever gods who dwell in the site of battle (of course, at the risk of more random/unpredictable magic).
I imagine in your world when civilization advances, they realized that best way to utilize magic in combat is by precision support strike by slow magic (from safe location far from the front lines), and by fast moving shock infantry that use fast magic (in the front lines). At this point, they have realized the theory of combined arms.