I can only give some insight to the LP/natural gas side of things.
The size of the regulator doesn't really make too much a difference. Many different manufacturers and they build various sizes dependent on its capacity needs. Very typically we see LP systems using copper tube because the supply pressure from propane tanks is much higher than natural gas. With LP/NG regulators, you typically will see a larger body size as they increase in BTU capacity. The regulator that you see in the picture might be specific to that motor in delivering the pressure (measured in water column, or w.c. abbreviated). It is likely going to be in the ¼ to ½ pound of pressure that is being fed into the carburetor (equivalent to a range of 6in w.c to 12in w.c.) depending on if it is NG or LP, with NG being the lower pressure side. The size of the gas line in this case, black iron which leads me to believe it is NG, is based upon what ever pressure from the supplying the gas utility, be it the propane tank or the NG company. While the pressure from an LP tank coming directly out of the tank valve is over 100 lb of pressure, it would have a regulator right there at the tank dropping that down anywhere from a half pound of pressure up to 15 to 25 lb, again dependent on how long ago it was installed. If it's a natural gas utility and the setup has been around for 20 plus years, it is likely a ½lb to 1psi delivery pressure. Modern day generators for whole houses will usually burn somewhere around 250k up to 500k of BTUs per hour, dependent on the load.