The difference between bright and woody, I would assume,, is the difference between how much string and pick (bright) you are hearing versus how much of the guitar's body...
It's sort of something you have to play around with to have points of reference.
It's like asking what the difference between green and blue is. If you've never seen them, it's impossible to explain it to you.
Also, there's the fact that, when I say "woody" or "bright," I'm probably conjuring entirely different examples of what those tones are than some other dude using the same words.
However, I think those sorts of tonal differences are gonna have a lot more to do with how you position the mic than with whether you use a SDC or a LDC, especially if you are putting the mics in the near field.
Not to say mic choice doesn't matter, but whichever you end up going with, knowing where to put it is priority number one.
Specific example: a mic positioned about six inches away from the twelfth fret, pointing straight at it, is gonna have a significantly brighter tone than one positioned about six inches from the bridge, pointing past the bridge and away from the soundhole. Try those two out with whatever mic you've got and see if any points of reference start to click for you.