We own and use both, and each has their seperate place and use. With canning, pressure or hot water bath, you are open to a lot more than you can be with dehydrating. We have two pressure canners and 3 hot water canners, and they're used nearly year round. (1 pint, 1 quart, and 1 half-gallon)
With canners, you can not only do fruits and vegetables, but meats, meals, jams, jellies, pickles, potatoes. and many other options. Pick up a copy of the Ball Book and look through the tips and recipes. The options are endless.
As some have said, you can get jars for free or really cheap. I've gotten jars from craigslist, freecycle, thrift stores, garage sales, and flea markets. To keep a good supply of rings and seals, get into the same habit with them as you would many prep items. Neither are expensive, so when you are at the store, grab a pack of each and put them away. It doesn't take long to have a good stock of them sitting when you need them. Also, I've seen some stores sell out at the height of canning season, so it's a good idea to have them on hand already.
Our vacuum sealer gets used for lots of things here besides food. I seal boxes of matches, camp meals (kind of my own MRE's), spare gun parts (with an oily rag), and many other things to put away for long term storage. You can do the same with vac-seal bags, and grab a box when you are at the store. They're a GREAT tool to have around.
Our dehydrator gets a lot of use, but not for things most others have mentioned. We dehydrate a lot of ingredients for cooking-onions, mushrooms, peppers, etc. It's been wonderful to have when I get free apples from next door, or marked down bananas from the produce store down the road. I slice chips or chunks and dehydrate them for snacks, or to add in homemade cereal. I don't dehydrate potatos simple because there's normally 60-80lbs of them in the unheated basement storage area.
All 3 are very valueable tools to have around. Look at each and look at what you plan to start with first. Pick the one you would tend to use most often, then go 1 by 1 to the other two. Eventually, you'll end up with all 3 and not regret having them.