I have used both LDC and SDC mics. The main difference with respect to recording acoustic guitars is the bass tends to be more dramatic on an LDC and I find myself notching out a lot of it especially if playing a large body guitar.
Of course, a lot of that has to do with mic placement. I find LDC mics more boomier for acoustic guitar recordings. While it's perfectly ok to use an LDC you might need to put in an EQ and get rid of some bass after you record it. No sweat.. I usually play a smaller body Martin which lends itself well to LDC recording.
Good pencil mics are the favored way. I don't have a good pair, so I usually resort to doing it with LDC and notching the bass.