I have a small genny (about 650W) which I fired up and ran the fridge and freezer (had to take turns, it didn't like it when they both cut in together) and computer and router.
I have monitored my fridge/freezer and freezer power.
Samsung RZ80 Freezer Idle 11W run 58W Defrost 276W.
Samsung RL60 Fridge Freezer Idle 9W run 53W Defrost 215W.
With both used a plug in meter which recorded Max Watts which was only reached when on de-frost cycle.
My mother however has a very small 30 litre freezer with no de-frost function run 28W but start 973W.
A old Hoover fridge/freezer run watts 82 but start 2259W
A smaller fridge/freezer at sons house was 170W run did not record start.
A small freezer as sons was 153W run and 719W start.
Power factor correction was as low as 0.75 with the old freezers.
The measurements were made with the idea of working out if it was worth changing an old unit to save power and it was not the cost of replacement over 7 years considered as normal life was not enough to make it worth changing.
But the single phase motors in the older units have a massive start amps. They also have built in overloads as if it tries to start before the pressure has dropped it will stall. Trying to run a fridge or freezer from a long extension lead can cause problems where the overload is being repeatedly tripped and in the end they fail. Likely it is one of the major reasons for them to be thrown out the over load has failed due to repeatedly being tripped.
The two Samsung models I have quoted has 3 phase motors and are started using an inverter the inverter/motor package has a 10 year warranty although that does not include the rest of the unit. The whole idea is if you remove the overload device you have removed a major cause of motor failure. This is as I have said more of a problem when using extension leads most freezers and fridges say not to use extension leads in their instructions.
You clearly have the same problem with a small generator. The fridge and freezer start current is the problem rather than the run current. Often having one motor running actually helps start the second one.
But you have to consider the damage being caused to the overload trying to run them from a small generator. At the cost of the Samsung clearly best option is a larger generator to get the start amps required. Only if an existing freezer or fridge was to fail would it be worth replacing with an inverter model.
The gas fridge with electric option uses nearly twice the power of an electric only model. However it does not have the start amps problem and can be switched to gas with a power failure they even run on 12 volt.
The peltier fridge is worst of them all it uses 4 times the power of a electric motor type. The only advantage is does not matter what angle it is used at or how much it is shaken so used as cool boxes in cars.
Gas fridge in a caravan uses around 200W on mains which is higher than any motor type but no start amps.
I don't know how often you lose power but if quite often I would say you need a bigger generator. Some of the inverter generators can be run in tandem worth considering. With inverter generators the speed varies with load so they use less fuel but not sure how they would handle the start amps. It is the same with other generators some will just cut out if you try to draw too much others can be overloaded and can burn themselves out. It really does seem to be pot luck which you get.