This will not be an all-inclusive study of the two preservation methods, just my quick thoughts based on my experience.
When I was growing up my mom canned and froze produce for the coming year's meals. But as I recall, she mostly canned fruits and tomato sauce and she froze the vegetables. Why was that?
For one thing we didn't have a pressure cooker to can at high heat and pressure. Fruits can at lower temps and don't need any extra pressure. Also, most fruits turn to mush when you freeze and then thaw them out. We made over a hundred jars of jelly/jam/preserves each year to use most of the fruit. She also made cinnamon apple rings (my favorite of everything she made).
We would pick, clean, blanch and freeze the vegetables. In a good year we filled two large chest freezers with corn, peas, green beans, succotash, and lima beans.
I can't even come close to those quantities. My garden is about one quarter the size and we eat a lot fresh from the garden. But so far this year, I have seven quart bags of green beans in the freezer and the fruits I talked about in a previous post. In addition I have two dozen onions dried and stored and many more in the garden. My onions matured far earlier than ever before so I planted new sets last week. They won't get too big, unless we have an unusually mild fall (fingers crossed), but you can eat onions at any stage of growth.
I only planted two tomato plants this year; one slicing tomato and one sauce tomato. They are both producing more than I can eat so tomorrow will be a sauce-making day. I'll use my own peppers and onions to flavor the sauce.
My cucumbers are coming in now and I'll make cucumber-onion salad, which is one of my favorite salads. I've tried canning it in the past but it gets too soft because of the heating process. I can make it and store it in the fridge for almost a month so that works for me.
I let some "volunteer" potatoes grow. I have no idea what type they are. I haven't planted potatoes in two years but these popped up from old spuds left deep in the soil I guess. It will be interesting to see what I get.
I ate bags of radishes in the spring and once the temperatures cool down I'll start planting my fall crop. I love radishes.
I find freezing much easier for vegetables. I have a very large upright freezer that came with my house when I bought it. The more full it is the more efficient it runs so I try to get as much food processed and on the shelves as I can.
Green Beans need to be blanched before freezing. I'm not really sure what blanching does but it is a must for long term storage. I blanch one quart of beans at a time. I use a large pot of boiling water. I drop in one batch of beans at a time (enough to fill a one quart freezer bag) with the timer set for two minutes. When the timer goes off I scoop out the beans and drop them into a large bowl of ice water. The ice water stops the cooking process so the beans stay crisp. I stir the cooling beans around in the cold water to make sure the beans are thoroughly cooled. Then I bag them up and place the bag in the freezer. I want them to freeze as quickly as possible so I spread out the bags to get cold air all around them.
When this is done properly, and it is fairly simple, the beans will stay edible for two years. I say two years because that is the longest I have ever had a bag of beans in the freezer and then ate them. Even after two years the beans were as good as fresh beans from the fridge. Just take them out of the freezer 2-3 hours before you want to cook them and let them slowly thaw in the refrigerator. Then cook as you would fresh beans but you can shorten the cooking time a little bit because they are partially cooked during the blanching process.
