It's how you blend the stuff.
I am a little iffy on this thing, but my instincts tell me to apply effects to the close mics.
and then blend it with the room mic. Or forgo the room and just use VST.
You should look into convolution reverb and find some OG plate impulse responses.
http://www.openairlib.net/
that site has some pretty dank stuff. That whole site came with a free update for the convolution reverb update, and they have some pretty awesome plate impulse reasponses.
I find that the beefy settings work really well on a drum kit.
I'm very wary on forgoing the room mics and simply replacing it with a room reverb plugin. I mean... I'm sure it would work out and I could just use a room reverb as an aux send on all the close mics. It's just that I kinda want to learn the more conventional practices before getting into anything crazy if that makes any sense.
Another thing I was also curious about is whether to start the mix at the overheads or the close mics. I'm also confused about whether to add the room mics after the overheads or after the close mics.
God mixing acoustic drums are so much more annoying than electronic drums. 
You should still look up convolution reverb....plate reverb is daaaaaaaaaaaaaank. and old school. So you're not selling yourself short.
It depends man. If you want more room, do more room, if you want more close, do close.
treat the room mics like as if it were reverb.
I try to emulate my reverb units as if it's a 3d space. But i mostly use plate reverb to get my dimension. and if i break my drum layers like i've recorded them. I'd have a close mic, and room mics.
and for what i want, i want my drums to be banging, so i make sure to prioritize the close mics in terms of volume. Then I toss each drum element on a buss plate reverb. So that it sounds cohesive.
From there i can manipulate things individually in terms of sound charcteristic. like adding two different distortion sounds on the drum, but still route them into the same buss tube distortion.
No different than using what you already know. The trouble is, actually getting a good recording. That's the only thing beign added.
And since most people aren't really going for a more "natural" sound like i am, you might have to rethink things to "how did they do this in the past?" and look up some old recording and mixing techniques.
