Most of the bigger mics I have came with a shock mount, but they also have the hard mount too.
I usually set up most mics with the shock mounts if they have them, but there are times when I want to get the mic in closer to the source, and the shock mount is in the way, so I just use smaller hard mount.
I don't notice any sound difference, but then, the floor in my studio is solid cement, so there's no vibrations, unless I was to hit the stand with my foot, which can happen when using the tripod stands with the long legs.