Don't have an outside kitchen set up any more, but always used a flat griddle or electric skillet outside. Our previous camper had a 2 burner outside stove and sink. Everything had to be brought out and then put up eventually. It would have been great to have had some outside storage that was readily available so we would not have had to drag everything in and out, and then back in again.
Current 5er does not have an outside kitchen at all, but we still have an portable stove that can be set up anywhere. We'll continue to fix meals, all of them, outside as much as possible.
In my opinion, initially stock the kitchen inside the camper as your primary kitchen. Then, when you start using the outside kitchen, bring out just what you feel you need outside and leave it there. Then slowly add a second one for inside. Or, if you find yourself doing meal preparation inside mostly, then just put outside those items you use on occasion.
If I understand right, those outside kitchen refrigerators are electric only and when traveling, they are not powered. The refrigerator inside is powered with gas or electric, unless you have a residential refrigerator. The outside refrigerator will not be practical to use for longevity items. Frozen foods and such will be kept in the inside refrigerator.
Basically, only you can really figure out what will work for you. You might not like the outside kitchen at all and never use it. And then, you may use it exclusively and never use the one inside. If it were me, I'd probably stock both. But initially, I suggest stocking only one completely and then moving things to the one you mostly, primarily use and over time, replace the second one.