In addition to freezing and canning you can also dry your foods, while this is a great way to preserve nutrients and provide a shelf stable product a dehydrator may not be something you have access to.
Most anything can be canned, frozen or dried with only a few exceptions, how you choose preserve your harvest will depend on things such as goals, taste and storage.
There are a lot of different things to consider when deciding whether to freeze or can, some of those considerations may affect you while others may not.
Choosing the Right Method
Goals - Are you raising food to stockpile or are you just trying to have enough healthy organic food for the winter? Many people who are stockpiling are concerned about power outages and the possibility that electricity may not be available at some point, because of that, they choose to store as much of their shelf stable as possible. This includes canning, a method called dry canning and dehydrating.
Those that are concerned with healthy organic food often freeze their food, the taste is often better, and freezing is gentler on your food than a pressure canner is.
Storage - How much freezer space you have versus space to store jars. I have 2 full freezers and 2 small ones; this gives me a lot of latitude in how much I am able to freeze. Currently I have one full with chicken for winter and one freezer I am loading up with vegetables.
Pantry space is more problematic for me, as our basement leaks; I have no root cellar currently and am storing my pantry in my bedroom at the moment. I try to spread my harvest out to utilize the storage space I have.
Taste - A lot will depend personal preferences, for instance, I prefer a canned peach to a frozen peach but would much rather freeze strawberries than have them canned. I like canned green beans but don’t really care for frozen. It does no good to can or freeze something if it is not going to get eaten so you need to use the method that provides a better tasting product for your household.
How your Food will Be Used – If you are going to use potatoes in soups or stews then canning it is a better way to go, if you want to make hash browns or French fries then you will want to freeze them.
Onions can be dried, frozen or canned, but will be used much differently depending on how you process them. Dried onions are great for seasoning recipes of all kinds, frozen are perfect to add to soups, casseroles and other recipes, whereas canned onions are typically pickled and are best eaten out of the jar.
Tomatoes are best canned, and certainly more convenient, frozen tomatoes are fine for throwing into pots for soups and stews, but tomato sauce, crushed tomatoes and spaghetti sauce will all need to be canned.
Budget - In the end a lot will also depend on your budget, we knew this year we would need two freezers because we had both a garden and chickens to process, so we put a new freezer into our budget early on. I would not even mind having a third freezer as it allows to bake and cook while things are fresh and put them in for use later in the winter, but then I worry about the possibility of having outages.
Jars can add up in price as can the cost of a good quality pressure canner, add the cost of building somewhere to store it all and it adds up fast. Canning however can be affordable once you have a canner and the jars, since all you will need to buy is lids and pay for the power usage. Another alternative is to buy reusable lids, expensive, but so is repeatedly buying lids each year for your jars. Jars of food can be stored anywhere that is not too hot or too cold.
A quality dehydrator is also expensive but is well worth adding to your collection of preserving equipment. The finished product if sealed correctly is shelf stable and takes up less space than canning jars do, and can be used in a variety of cooking techniques.
Keep in mind when freezing or dehydrating, how you package your produce matters, the use of quality sealing devices and the right pouches is essential if you want your food to last. This all costs money as well, and should be considered in your budget.
In the EndI chose my preserving methods based on what was most affordable for me this year, we have a generator so on the short term if the power goes out our freezers and produce will be protected. I have freezer space and limited jars, so I am saving my jars for those things that are not easily frozen, such as chicken and vegetable stock as well as tomato and spaghetti sauce. I plan to use my dehydrator a fair amount as well, especially for herbs, onions and garlic, but also for other food items that can be used in soups and stews.