Crunches are said to be more effective because you only work your abs. The extra distance you move when you do a sit up you're only putting strain on your back and working the abs minimally.
IMHO, that ab machine you spoke of is VERY effective in creating a burn, if done right. When you lie on it, your arms and head should only be RESTING on the support points. When you crunch, only squeeze your abs. Once you crunch up, hold it there for a second, then slowly move back down, but not all the way, keep the abs taught throughout the whole workout until you feel like your abs are gonna melt and it hurts to even breath.
However that said, you may have the biggest abs in the world, they wont be impressive unless you get rid of th elayer of fat above it.