Why aren't you using your best spell all the time?
Whatever throttling system you're using it has to answer that question. How it answers that question should be in line with the ideas the game has about both magic in specific and the PCs in general. Think about:
Research, lateral (low-angle) to vertical (high-angle): What does discovering new spells do for your mage? Are they improvements on spells you already have (vertical) or new capabilities that you didn't have before (lateral)? This also includes character advancement that focuses on improving a single spell.
Development, low to high: How do your spells improve as you become a better mage, improving core magic skills and other attributes? Is most of a spell's power in a spell itself (low), or can a more experienced mage get much more effect out of a spell than a beginner (high)?
Escalation, low to high: How does the scope of what you're capable of doing increase over the entire game? Do you start out capable and end without tremendous jumps, aside from maybe a mid-season upgrade (low)? Or do you start out using magic to throw stones and force stuck doors, and end by using it to rain down meteors and breach other planes of existence (high)?
Spell slots: "I only have a few of those."
Research: mid- to high-angle Development: low to mid Escalation: mid to high
Let's get D&D out of the way first, because everybody knows that one. Spell slots are a decent way to manage a caster who'll be at very different power levels as the game progresses, by keeping the number of "best spells" they can cast fairly constant even as they get more slots of all levels.
Part of this high escalation is that acquiring new spells is an important part of keeping up your relative power in D&D, which is why you get at least a few automatically in later editions. But let's talk about those earlier editions to introduce the secret fourth thing you should think about, Budget.
In its earliest incarnation, the magic-user was a unit in Chainmail, a fantasy tactical wargame, which was itself a new sort of thing and operated by analogy with other war games of the time, such as sharing terms like "armor class" and "hit points" with naval tactics games. The magic-user was an analogy to the artillery piece, a unit capable of having powerful effects over a wide area, which was limited by its stock of "ammunition" - spell slots.
But an important element of a symmetric tactical wargame is that the artillerist knows the total enemy composition that they have to affect with the supply of shells they have, and they can ration their shells appropriately instead of just firing to little effect at tiny fractions of the enemy force. With the move to an asymmetric game where the total enemy composition is unknown, there's a lot more uncertainty about when spell slots should be used before you get a chance to recover.
Mana: "It's not the only thing I'll need to cast."
Research: low-angle Development: mid to high Escalation: low
Mana works better in systems where the power of the magic is more in the mage than in the spells they cast. This probably means you're not going to do a lot with qualitatively different "high-level spells", because you run into a cost problem.
A spell that's twice as powerful as another spell should cost more than twice the mana - it's not only twice as powerful, you're getting the effects in less time. If you create a big difference in power between spells, the cost difference is ideally exponential.
If you have a large range of costs, that also creates a bit of a granularity problem - sure, you have the power to impose very finely gradated costs, but with great gradating power comes great gradating responsibility. You can look at a 2nd-level spell in a spell slot game and ask "why isn't this 1st-level or 3rd-level?" and probably get a fairly sound answer. Can you say the same about looking at a spell that costs 6 mana (out of a top cost of, say, 200) and asking "why doesn't this cost 5 mana, or 7?"
Even if you keep the range of costs and the power of spells (as opposed to the mage) in a fairly narrow band, there's still the budget angle to consider. The total opposition isn't any more known than it was under a spell slot system, and the flexible nature of mana means you have the ability to completely dry yourself out, to an extent you can't under a spell slot system, effectively upcombining lower slots in fives and tens to get one more big boom.
Backlash: "I would literally die."
Research: Low- to mid-angle Development: high Escalation: low to mid
In a lot of ways a backlash system is like a mana system with a discount. But what this opens up is the ability for that discount to grow as you develop, allowing there to be more powerful spells that you cast without as much of an increased cost. If the effects of backlash are exponential, you can have a linearly developing cost system and resist skill that still impose exponential costs.
In addition, a backlash system can get around some of the budget issues -- you still don't have any idea about the total strength of the opposition, but you can at least avoid beating yourself up with backlash any more than the rest of your party is getting regular-style beaten up. The ability to cast some spells with a high chance of being free also means that you're never completely empty, at least if you're willing to risk a little.
A backlash system also has some interesting angles if the game's got some kind of narrative metacurrency you can use to improve various rolls. An artillerist isn't going to suddenly be able to will more shells into existence just because their brother's on the front lines fighting the villain who killed their mother, but if you're operating under a backlash system and can boost your resistance roll, that effectively lets you "find more magic" by getting something powerful for free.
A final note: Call of Cthulhu and "lifetime mana".
Many caveats about the mana system don't really apply to using Sanity to cast in Call of Cthulhu. Everything else I've been talking about assumes that whatever you're using up to cast magic, you can get it back. That's not really something you can say about Sanity. Getting even some lost Sanity back is risky and expensive, so you may as well be losing it forever, and as a result spells aren't necessarily "balanced for Sanity efficiency" because you'll only use them a few times in your life.
But that fits the general tone of Call of Cthulhu - a nigh-incomprehensible doom awaits the world, and all you can hope for is to push it back, even if you lay down your life. The magic system is a means to voluntarily break your mind to give the future hope, in the same way a more physical character could make a valiant sacrifice and voluntarily break their body (and their boat, and a satchel of dynamite).
