Well... i don't search anymore for "similar" music. Most times i did it i have been disappointed by results.
I like APC too, but more than liking what they share with Tool, i like what they don't.
Having a
look at this, you won't find that much matching your question IMO (lots of great bands there, anyway).
The only band i would tell sharing similar mood and problems and sound (except for voice) in that map is Opeth, for which i can suggest Blackwater Park (although i know only an half of their discography).
Another at-any-degree similar band is the czeck Animé, which you
can listen to. I'm not advising them, it's just an answer to your query.
If you want to listen to something different, with very heavy feelings, try Sunwar the dead, by Elend. You need a good hi-fi, but it can crush your spirit. It's like someone who is having not a happy day without making me think about youth problems (which most bands do). Something you will love or hate.
On the genre Tcube advices, i liked "Melody A.M." a lot, by Röyksopp.