Generally, it’s fine to ship any item by any of the modes we regularly use. All orders are carefully packed, and fragile shipments are marked as such.
We use only clean, new packing materials and our standard is that the package should survive being dropped from a height of 4′ onto a concrete surface, at any angle.
For the record, we did have a damage claim rejected on the grounds of inadequate packaging. The package was thoroughly crushed, and there were tire tracks visible on it. UPS maintained that the packaging was inadequate, and since we cannot routinely pack orders well enough to survive being driven over by a fork-lift, we no longer use UPS.
We can detect no correlation between shipping mode and the risk of damage– the incidence of damaged shipments is too low to be statistically significant. But we suspect that the risk of damage increases with the time that a shipment is in transit. Which makes sense when you think about it. A two-day package is probably handled less often than one that is in transit for a week.