The better question is what are the differences between a rigid fork mountain bike and corresponding hardtail with suspension fork. If you ride slowly and carefully enough, and providing that you can get the same dimension tires (a huge "if"), and you're strong and technically skilled, the differences aren't that much.

If you ride aggressively, the differences between a quality front suspension and a rigid fork become quite pronounced for ground tracking, stability and bite when the $#it hits the fan.

As for road hybrids and suspension fork hybrids, they're different entirely. They don't compare well to what a good MTB can do. The differences are like between Honda Pilot and a HUMVEE. If you want to drive on an improved gravel road to your favorite winery, then they're equivalent. The Honda will be quieter and more comfortable. If you want to go over stumps, ford streams and rockbeds, and plow through saplings, all at speed, then don't take your Honda.