One way or another, your spell-cast IS a better spell-caster if he is only one class.
The difference is too marginal for my tastes; the vast majority of your spellcasting power comes from just the basic spellcasting move and your level. It's the earlier access to the more powerful spells which really starts altering the face of the game; most of the advanced moves around spellcasting are just frosting, the best (in my opinion) being the Cleric's Serenity tree, allowing the ignoring of ongoing -1s for maintenance.
The warrior-mage build is pretty over powered using the standard rules, actually. (I'm thinking dex-based elf fighter (for always precision weapon racial move) > takes wizard casting at level 2, at level 7 he has +3 Dex and Int, giving him +3 for Hack and Slack, Volley, casting. He's ridiculously armored after he grabs Arcane Ward with Multiclass Initiate, casts as a 6th level wizard, and hits like a truck (probably 1d10+1d8 base damage presuming you've chosen Merciless > Bloodthirsty.)
I actually think once I finalize and implement this system, I'm going to disallow the Fighter from picking up spellcasting with his "Multiclass Dabbler". It's just too powerful. The fighter is the only one I think it's a problem for, though: it makes sense for the Bard to grab it, and it fits better both power-wise and thematically. The rest of the classes don't have multiclass moves at 2-5, I don't think. The Ranger and the Paladin have their special cleric spells move, which is fine and thematic.