It depends on your mood!
APC is a bit more shallow, yes, a bit more mainstream, but it still has Maynard, and it still has rockin' instrumentals and lyrics, they're just more pointed, obvious, and plain. Judith, Magdalena, and Counting Bodies Like Sheep come to mind. Magdalena, by the way, being the most eloquent and beautiful stripper song I've ever heard.
You can rock-out to APC, but you experience Tool.
Tool for introspection and big, wide world of criticisms of humanity's faults, and always poetic, yet never requiring words to rhyme to sound so undeniably "sung". Hooker with a Penis, Part of Me, Prison Sex, Aenima, Stinkfist, Opiate, etc. I'm not too keen on 10,000 Days aside from Jambi, since I don't see the staying power of the aforementioned songs, but I still appreciate the points he makes.
TL;DR: APC when you're FPS'ing, Tool when you're lying on your bed wondering "what does it all mean?"... or when you finally decide to try mushrooms and chill in your living room at 2 AM with friends just watching the furniture breathe.