There is actually two issues involved with generator set stability. One is "steady state" or how well the governing and engine dynamics maintain engine speed with no load changes, and "transient response" which is how well a unit responds to a load change.
Most manufacturers these days conform to ISO 8528 part 5, and will call out a class of performance they meet. ISO 3046 part 4 has guidelines for engine speed governing.
In reality, stability is a function of the integration of the governing and the engine mechanical response. A mechanically governed engine may have a fairly poor steady state stability of 3-5%, and some hydro-mechanical governors can be better than 1%. Electronic governors are usually much better, but rely on an electric or hydro-mechanical actuator to control the fuel system, and this usually reduces the stability somewhat, but in general, electronically governed units have better steady state and transient response than emchanically governed units. But the best electronic governor in the word can't make a poor mechanically responding engine any better. There are also the issues touched on a little in the previous posts such as droop or isochronus governor operation. And the newer engines have the governing imbedded into the engine ECM, and just because it is electronic doesn't make it the best electric power application governor.
A lot of facilities use really new and neat power conserving and highly efficient machines, and on utility they work just fine, because especially here in the US most utility power is very good by most anyone's standards (and yes, I'm sure there a few exceptions), but then a backup generator is installed, and usually it's selection is driven by price, not performance, and when the unit is tested, or worse just actually used in an outage situation, and things don't work in the plant, people start to wonder what is wrong with the generator.
A lot of available equipment has either a hardware (jumpers or switches) or software adjustments to allow for wider frequency and voltage tolerences depending on stability of source. If your equipment doesn't have that option, and you need a backup power source, then integrating some form of power conditioning or UPS will be required.
Any standalone generator will have frequency and voltage variation, both in "steady state" and in response to load change. How well it provides stable operation is a function of system integration, engine/generator/control selection, and installation.
These two links have some pretty good general info, and most manufacturers have more detailed information in their sizing and application guides,
Now I'm not a Cummins guy, but sometimes their technical papers are very good, hope that helps.