Similar to many areas where opinions differs strongly, Generators and Inverters both have their place in the electricity supply arena and there is no single correct answer. Generators able typically able to supply heavier loads than inverters and are relatively more portable. They are however very noisy, (even the Silent ones!) and are being prohibited by many Body Corporates for use in complexes.
Using fossil fuels makes them environmentally unfriendly and costly to run.
They are very inefficient when not being used at close to maximum delivery capacity. This is because the engine uses almost the same amount of fuel when it is under load as when it is not. As with any engine they must be regularly serviced.
More often than not generators are oversized for their average load and need to be because they cannot handle surges in power demand.
Inverter systems on the other hand do not cope as well with supplying the very heavy current loads i.e. washing machines, tumble driers, Air conditioners, heaters, etc. because of the large heating elements these devices employ. The high current demand drains the batteries much faster than with lighter loads and therefore require much larger battery banks.
Light continuous loads and shorter term medium loads on the other hand are ideal for inverters with the correctly sized battery bank and the correct solar array.
Inverters are virtually silent and are much better at dealing with a surge in power demand such as happens when motors and pumps, etc. start. Almost all can deliver at least twice their average load for a short period.
In the short term purchasing a generator involve less capital outlay, but in the medium to long term, the cost of ownership of an inverter, battery, solar panel system deliver a far better return on investment and have a lower environmental impact.
I see the most probable outcome evolving with the deployment of hybrid systems which use inverters and solar charged batteries supplying all low and medium loads with the generator (or the Grid if it is stable enough) used to provide backup power to solar for the rainy days and to supply the higher demand appliances.