4 conductors allows you to do crazy stuff like series and parallel wiring. It's not 100% necessary, but I guess it's nice. Most pickups have this.

Single conductor has one wire coming out, wrapped in this shielding. It's easier to connect, but that's all I can say for it.
Don't Griffin's have the ability to do Coil-tapping? if so, get the four-conductor one, so u can keep the coil-tapping and not have a weird push-pull pot that does nothing.