Looking at arcane and divine magic in ACKS Core, the real difference isn't between what sort of spell effects they can generate. Divine gets Flame Strike and Spiritual Weapon, and Arcane gets Reincarnate. The real difference is one of philosophy.
Divine magic is half-assed. It either solves a problem so specific that you have to go looking for situations to apply it in (Snake Charm, I'm looking at you), or it solves a particular level-appropriate problem unreliably (Fellowship), or it sort of helps you solve a problem but doesn't solve it all the way (Bless). Fellowship and Charm Person both aim at the problem of "I want to make friends with this weak sentient monster", but Fellowship has a decent chance of not-working or backfiring, and even if it does work you're still at the mercy of the reaction roll. It helps, but it doesn't solve the problem all the way. Bless does the same - it makes combat easier, but you still have to do a bunch of work (contrast with Sleep, which solves the problem outright). This is true of the Cure spells too; they help extend the adventuring day a little, and might keep somebody from dying, but they're honestly not all that much healing when spread across a party. Apparently gods are lazy. "Listen, bub, I have like a thousand other equally-unworthy petitioners to help today. Be grateful for the gifts you have received, and know that I help those who help themselves."
Arcane magic, on the other hand, is what you get if you put a bunch of engineers on solving a problem with a very large budget and no supervision by management, marketing, or people with common sense. Arcane magic totally solves the most-general formulation of the problems it sets out to solve, but it also creates exciting new problems in the process, in the idiom of "... huh, we didn't consider that when we designed this thing." Charm Person, for example, solves the problem of making a weak sentient monster your friend pretty reliably. It also creates a some new public relations problems, when your new buddy wants to come with you back to town. Fireball is the most literal expression of this collateral-damage idiom. Disintegrate obliterates your target, but destroys any treasure he was wearing. Swords and Wizardry's version of Fly, which has a variable duration and no soft-landing clause, is pretty good, and Haste and Reincarnate are great examples too. "You want us to to bring him back from the dead? Totally, we can do that. We'll make him bigger and better, overclocked, liquid-cooled, with neon-lit casemods and a spoiler... Look, I really don't understand what you're mad about, your old race wasn't that good anyway. Seriously, gnome? Why would you want to play a gnome when you could play a cyborg bear with liquid nitrogen for blood? Language? ... hm, interesting point. We can set you up a speech synthesizer if you want; as a matter of fact there are a number of new technologies I've been meaning to <mauling and screaming>"
Wizards and engineers: turning every campaign into Gamma World since forever.
Anyway, these two approaches are balanced by relative repertoire size / spell availability; a cleric can half-solve lots of different problems, while a wizard can overkill-solve a handful of particular problems that he's prepared for.
The secret third flavor of magic, thief magic, solves precisely the noncombat problems posed to it, with no noise and no overkill, but is highly unreliable.