"I know that one part of the process is that they vibrate or shake the one piece agaist the other for 30 min" - this is ridiculous. I am an engineer and formerly worked at a company that makes stone countertop machinery and this is simply not correct.

there are a few things that make a perfect seam:

1. the edges to be mated must be perfectly vertical and flat. there are a few ways to accomplish this depending on the fabricators equipment. many shops only go "1/2 way" and skip the steps that make the edges perfect.

2. the top edge of the seam must be chip free. again there are different ways to accomplish this but many shops simply leave the edge irregular. you see pics of this often on GW. Not all stones can be make perfectly chip free but most can if the fabricator is willing to take the extra time. The main reason quartz seams look so good is that the top edge doesn't chip even with simple sawing so it doesn't take extra effort to make the seam good.

3. a perfect seam is perfectly flush across it's entire lenght. This can be impossible as natural stone slabs are often not perfectly flat. Quarts is better in this respect because of the way it's manufactured. when there is a step at a seam a good installer can often eliminate most or all of it if he has the correct seaming tool which actually allows him to bend the stone very slightly. Some granite shops will grind a seam after install but IMHO it can be near impossible to work the top surface such that the worked area is invisible from every angle in every lighting condition. (Note: some fab shops regularly grind seams and say it turns out perfect. I'm a non believer.)

4. The grain transition across a seam is often the most conspicious aspect of a seam. Good fabrication minimizes this but it's almost never perfect. Again quartz has an advantage since even the newest quartz colors have very little movement compared to actual stone.

5. the exposed edge of a seam should be flush on the bottom. since slab thickness can vary sometimes the fab shop has to grind the underside of the pieces meeting at the seam so the bottom of the joint is flush. Only a hack shop leaves a step on the bottom of a seam.

May I ask whether the equipment/method necessary to ensure a vertical, flat and chip-free edge is something that most fabricators would have, or does this process require expensive equipment that only the larger fabrication companies would have?

Most shops, even relatively small shops that only do a few kitchens per week would have the necessary equipment. A bigger problem is that many shops don't spend the extra time it can take even though they have the equipment.

How does hardness or softness of the stone (guess there's middle territory there too) affect the seam making when working with granites?

only to the extent that hardness correlates with "chippiness". in general harder stones are "chippier" but it's not a consistent relationship. Some relatively soft stones chip because the inclusions pop when you saw it.

hope this was helpful