Whatever you do, a second battery with a manual or automatic isolator system will go a long way to at least protecting your starter battery from being run down..
A lot depends on how long you want the refrigerator to run without the engine charging the battery. If you're looking to park the rig for long periods of time during the day while your off hiking or biking somewhere, then a good high power solar system could potentially power the refrigerators, with minimal draw on the battery for hours at a time. Just remember that solar panels rarely work at their peak rated output, so if it's rated for 50 watts, you'd probably be lucky to 25 watts out it average at any given time throughout the day. Although you're better off in Arizona than a lot of a places. 25 watts will not completely power the refrigerators, so there will always be some draw on the battery. Also, at night while camping, you'll be fully drawing from the battery if you decide to leave the refrigerators on and the solar panels would be useless.
If you spend most of your time driving around with only short stops, then neither a solar panel or generator is going to make much difference, since the draw on the battery will be minimal during the day and constantly recharged as you drive around.
For night time use, the alternatives are letting it run off the battery all night long and then recharge the battery as you drive around the next day, in which case you'll need a good deep cycle battery, or get a generator and run the generator all night long. While the Honda EU1000 is quiet, it still makes noise and I personally wouldn't run it with neighbors nearby. I also would hesitate to run it all night long and instead would likely only run to power camp while I'm up and about, cooking dinner, etc, then shut it off just before I went to bed and run the refrigerator off of the truck battery…or turn the refrigerator off. I've found that unless it's excessively hot at night, my Engel stay pretty cool over night inside even when it's not running. If you need a full freezer to operate all night long, then a generator will go a long way to keeping it frozen, especially in hot weather overnight.
In my opinion, for multi-day use without using the vehicle to charge up the battery, a generator is the only way to go. You'd need to some serious solar power and good environmental conditions to keep the battery charged up and then it would only be charging less than half the day, while you're use would be potentially using the power all day and all night. Solar panels are better for burst loads, where the system goes through extended periods of time of no load, giving the solar panels a chance to charge up the batteries.
But if you plan to run the vehicle every day, then a generator just to run the refrigerator is not needed. It can be useful to power other things and as an emergency back up, however.
To sum it up, as someone who recently purchased both solar panels and a generator, if I had to choose between the two, I'd easily give up the solar panels and keep the generator, just because it's more versatile and powerful in an emergency. But a duel battery system is first and foremost long before I would consider the gen or solar.