For sure weights stored on railcars on hilltops (no existing commercial installs I know of) ... or the already widespread pumped-water storage ... would take a few seconds to come up to speed (compared to the 100ms for the Tesla). So clearly the battery will always win in unplanned outages.

Near-term, the batteries will probably be more expensive (replacement) than well-maintained mechanical/gravity systems. Longer-term, upcoming battery solutions may erase that advantage.