Tubescreamer - Symmetrical
SD-1 - Asymmetrical
The difference is symmetrical is smoother and less toothy, while asymmetrical is more aggressive sounding and supposedly closer to an actual amp (amps apparently distort asymmetrically)
If I had to hazard a guess, I'd say the OCD clips asymmetrically. The Voodoo Lab and the TS808 are going to use symmetrical clipping though, and that's 2 out of the 3 pedals you mentioned liking. If the guy can custom build you an overdrive, see if he'll install a switch to flip between asymmetrical and symmetrical clipping. It's a very common modification for most overdrives.
You might also want to look at the different diodes that are used in clipping circuits. The traditional tubescreamer ones are great, but there are tons more that all sound great and different - Germanium Diodes, LEDs, and a ton of different diodes that are only known by their part designation (i.e. 1N4001, 1N4372, etc.)
The diodes in a clipping circuit have a significant effect on the sound you're going to get out of an overdrive.