I always come back to LDC for some reason. Even if im rolling off the lows, Although a SDC most likely has flatter response and perhaps a tiny bit better high end detail I think at first listen most SDC's sound boring to me and that's probably my reasoning for using LDC.
Have used LDCs for OHs quite a lot, they are a lot looser and can definitely build up a lot more high mid gunk, I think they give a more realistic picture of the kit as a whole although this is not necessarily what you will want.
When using room mics, I prefer SDC's as overheads. Using them almost as close mics in such case. When using (mostly or exclusively) overheads, I love LDC's.
Depends on how I'm placing things and what sound I'm going for, but more often than not I'll use LDC's or ribbons. A couple u67's in an x/y or spaced pair is usually my starting point. I usually mic things so that the overheads comprise a big portion of the sound.
I like LDC's lots as overheads. Lately I prefer the full range, full kit overhead sound as opposed to the "mostly cymbals" approach. Unless you're moving from DPA's to u47's I doubt you'll notice a huge difference in transients.
Shot out Oktava MK012, Neumann KM184 and Audio Technica AT4050's for overheads on a pop punk album recently. AT4050's really gave a nice full sound of the kit from top to bottom and a wider stereo image compared to the other two. Going to be using LDC's on overheads more often I think!
I used to use the 4050's in my old studio. It had a smaller room and the 4050's worked well in there for a nice tight agressive sound. Good for metal, hardcore, punk. My new room is massive 30x50, and the U87s do an amazing job.