Like Slaction said, there can be a difference, but the type of switch being used determines how much of an effect it will have. If you are comparing red or blacks, there is probably little to no difference. Browns you might see some, but blues you can really tell.
On my Filco, the stock case compared to the Vortex aluminum case, blues sounded sort of hollow and cheap. Keep in mind, the stock Filco is a nice case and did not sound bad, it just sounded bad compared to the Vortex. The Vortex on the other hand, had a solid sounding click and feel and did dampen the noise in the room, but reflected more back right at you (which is why it seems to amplify pings). So about as noisy for the operator, but quieter for those around you. Adding a bit of foam in the bottom helps dampen the sound further.
Plate type, shape and thickness can also have an effect, as can how the plate is mounted. On mine I have an extra thick stainless plate, and have plastic dampers on the perimeter dampening vibrations from it, plus foam in the bottom. Then you have key caps (double thick PBT's aren't just for durability) and o-rings which can alter sound as well. Basically, you can tune the sound, just like the switch.
As Bucake also said, how it can bend and squeek, they can also rattle and rock on desks. A heavy aluminum one will sit more stable than a plastic one skirting all over. I have yet to find a keyboard as satisfying to use as my Vortex Filco. It stays put, has a solid sound, and ZERO flex... My KBT Race was nice, but now, it feels like a cheap plastic toy due to flex and lack of weight. So how stiff is the Vortex, it makes a Model M feel like a cheap rubber dome.
