Hi Steve,
You really want to do 2 different things and at least need 2 different types of "charges" in the tumbler. Steel shot with the right detergents does a very good job with silver or GF pieces. The shot actually burnishes the surface. As you say it hardens it and polishes it.
Some beads (but not all) will be chipped, scratched or dulled by the steel shot. The right detergent will keep the shot from rusting. GF usually requires a different detergent than sterling. Most rock shops or tool suppliers like Rio Grande sell soap mixes for specific metals.
We polish our charms, hand made ear wires and jump rings with a rotating tumbler at Rings & Things.
The vibrating polisher does work faster. I don't think it burnishes silver rings as well as the rotary.
For stone or glass polishing you usually use different types of media, often abrasive plastic shaped pieces. Instead of soap you use a cutting or polishing compound - things like Lindy A, tin oxide, etc. A rock shop, or better a rock hound club could tell you what they use for various types of stones.
If your primary use is silver rings, I'd suggest a rotary tumbler with several barrels. Keep different charges in different barrels.
If you want fast polishing of stones and only occasionally polish silver rings, the vibratory polisher would do both. You'd need to clean the body and change the grit to shot for silver.
Ultimately, you'll want both types. If you go for vibratory, look at the flow through type vs the solid barrel. There are advantages to both. Rings & Things doesn't carry either type. Perhaps other forum members can offer their suggestions?