Are drawers more convenient than cabinets? That's the question you're asking.

Third option, if you don't really need it to be under a counter would be to put a door style fridge higher, with storage drawer(s) underneath.

It's easier to see the labels on bottles and cans on a shelf...if you don't mind scooching down to see the shelf. I keep ale and some soda in the bottom drawer of my drawer fridge and don't have a problem with finding them, even if I have to pick up one or two to check the label. But I'm usually the one pulling things, so it's probably because I remember where things are.

With drawers you only get two surfaces. You can add baskets, interior shelves, etc., but that's not the same. If the compact fridge has several height adjustable shelves, it might hold most of what you want held without stacking.

I have some relatives who recently got a GE compact fridge. One of the big ones that.s over 4-5 cubic feet capacity. It holds a lot! GE was acquired by the Chinese company, Haier, recently. They've started selling some of their own design products under the GE name. The fridge my relatives got is an old GE model with excellent reviews. Who knows what the customer service situation will be in the future, but they're pleased with their fridge. I could make do with it if it were my only fridge.

I love my fridge drawers, but I think for your use it's pretty even as to which is more convenient. The quietest drawers (and probably compact door fridges) are SubZero and Perlick, but those cost as much as a full sized fridge. I don't know for sure, but I think the same quality drawer fridge as the GE compact might cost a lot more.