SDCs are the traditional choice for overheads because of their theoretical superiority in reproducing transients, which is important for catching the stick attack on ride cymbals, hi-hat, etc. This is not to say that excellent sound can't be captured with a LDC, or even a high quality dynamic. Some of the dynamic mics have a nice, almost silky high end. I've used a Sennheiser E835 dynamic - about $100 - for overdubbing ride cymbals, and it sounded wonderful.
BTW, have you heard about the Karma K-micro? A killer little SDC. I own eight of these mics, and they're a knockout deal for the price.
http://www.karmaaudio.com/products.html