AS&SH remains close to AD&D and has clerics and magicians. However, personally I quite like the idea of magic not being divided into arcane and divine spells and simply being magic. My favorite settings when it comes to magic are the Hyborean Age, Star Wars, and Dragon Age, which all don't make such a distinction. I've had a couple of lectures and seminars on historic conceptualizations of magic in various cultures at university and at least as far as Europe and Africa go, the difference between magic (arcane magic) and religion (divine magic) seem to be primarily one of application. The priest is an intermediary between the community and the world of the supernatural, using his training and education to maintain harmony between the two. The wizard, as far as others are concerned, is a professional service provider who compells the supernatural to intervene in the favor of his customer for payment. Methods and concepts of the supernatural world are almost indistinguishable outside of strictly maintained monotheism. And even in Europe, pagan traditions of magic survived well beyond the middle ages and were included in christian practice. The casting of spells and sacrifices were okay, as long as a christian priest was doing it for the benefit of the community.

And I am considering reworking the spellcasting classes for my campaign as well. The two main archetypes would probably be the magical scholar and the spellcasting warrior, which would be well represented by the magician and the warlock class.
Magician subclasses could all be retained. Monks are not affected, as they don't have spells, and priests and shamans become redundant. The one open question would be druids. They have more spells, hit points, weapon and armor proficiencies, and better FA than magicians, as well as shapechange, but require a lower amount of XP. Since they are basically better at everything, they probably would need to have their XP requirements significantly increased.

Turning Undead would be exclusive to necromancers, but that would not have to be a bad thing.

What I consider a bit more unfortunate is the loss of relevance for Wisdom. Without affecting priest spells, all it really does is a slight adjustment to Willpower saves if it's lower than 7 or higher than 14.

Most of the work would be reworking the spell lists.