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In essence this relates to weapon damage from creatures using "identical" weapons: A human's long sword does 1d8 damage, sure, but a storm giant with a proportionally sized long sword shouldn't do merely 1d8 damage plus its strength bonus simply because it's described/shaped like a long sword.

So a pixie is Tiny while a human is Medium and a dragon is Gargantuan in size. In a scenario where you have all three lined up at a target range and they're all, say, 10th level casters, would the size and effect of their fireballs be identical in scope?

A pixie is a little, itty bitty creature. For it to cast fireball and for it to equal the size and destructive ability of a human caster's fireball would seem overpowered.

Likewise a dragon is a mammoth creature so if it cast fireball you'd expect the magic it channeled to be much greater than a standard human caster's fireball.

Magic is unaffected by creature size. Creatures can have benefits for particular types of magic (it’s easy to imagine a dragon getting bonuses on fireball—after all, their descendants do—or a pixie getting some benefit with illusions), but nothing automatic just for being larger. Any such benefit would be listed directly in the creature entry.

For reference, this is also consistent with previous editions of Dungeons & Dragons. The premise, presumably, is that magic cannot be judged on physical grounds, and it’s in magic’s very nature to surprise you.

They would be equally powerful, as magic effects aren't affected by caster size, only by spell level. The description of fireball says:

Each creature in a 20-foot-radius sphere centered on that point must make a Dexterity saving throw. A target takes 8d6 fire damage on a failed save, or half as much damage on a successful one.

[. . .]

At Higher Levels. When you cast this spell using a spell slot of 4th level or higher, the damage increases by 1d6 for each slot level above 3rd.

As you can see, there is nothing in the description that says that damage is affected in any way by the caster's size, only by the level of the spell slot that they are using to cast.

Spells only do what they say - if they don't say they change based on the caster's size, they don't change

Magic isn't like a sword or other physical object. It has its own rules, and part of the appeal of magic in the first place is that it allows a lowly human being to achieve things comparable to dragons and other mighty creatures. In general, how big you are has no effect on the power of the magic you can wield - that's a function purely of your own magical skill and talent, as represented by your character/caster level (and so the level of spell slots you have available) and your spellcasting ability score.

Unless the spell says that its effects vary based on the caster's size, it will have the same effect for a caster of any size.

Maybe not "the same," but not because of creature size

There are many different kinds of magic in the world of DnD: divine, arcane, psionic, innate, etc. But when it comes to a creature's spellcasting (when not done through a magical item or other external means), there's a common theme: a spell's power and precision are bolstered by the heart and mind, not the body.

Every creature in the Monster Manual, and class or race in the Player's Handbook that can cast spells does so with a spellcasting ability of Charisma, Wisdom, or Intelligence. None of these are Abilities which are guaranteed to increase with size (a Tarrasque has between a +0 and a -4 in each of them). But they do tend to vary from one creature to another. Some dragons are far more charismatic than others by default (Gold dragons especially), and pixies tend to be more intelligent than white dragons, as a rule.

Likewise, a creature's proficiency bonus, which is essential in determining both its spell save DC and its spell attack modifier, does not necessarily correspond perfectly with its class level. For example, a Drow Mage (MM p. 129) is a "10th-level spellcaster," but seems to have a proficiency bonus of +3. A 10th level adventurer (player character) would have a proficiency bonus of +4. Proficiency bonus is also not reliably related to size: an Awakened Tree is a Huge creature, but only has a proficiency bonus of +2 (MM, p. 317).

All of this means that a spell may be "more" or "less" powerful when it is cast by two different creatures, even if they have the same spellcaster class and level: but only because the saving throws will be more difficult to pass, or the spell will be more likely to hit. And these differences will not be directly related to the size of the creature casting the spell.