To can or freeze primarily depends on intended use and freezer space..... though having a freezer go bad or a long power outage can result in loss of all product in a worst case scenario. So canning some and freezing some guards against that.
I don't do anything special to the meat, nor does it have any different taste really but it does shred easier than fresh bird. The biggest benefit is that even a skinny bird or an older bird becomes soft and easily used rather than needing special preparation to make it chewable or appetizing.
We like to do a lot of stir fry and other recipes that call for chunked chicken. Having it already cut up and ready to go into a recipe on short notice makes it simpler for meal prep if I have forgotten to get something out to thaw.
The canning process actually cooks the meat so you can even have it as is out of the jar, we do a lot of fresh salads which I add chunked pepperoni, ham and/or chicken to for a meal, and DH likes 'chicken salad' sandwiches, so all it would need is dumped out of the jar, drained and just add mayo and any other wanted ingredients for a quick lunch.
Our first run of the canned chicken was 5 extra roosters, we stripped all of the meat off of the bone without any real effort, and processed all of the normal 'scrap' right away in a large bulk to make our 'chicken balls' to feed back to the birds or give to the dogs as treats over their food. By doing all 5 roos at the same time we ended up with about 15 cupcake sized servings of protein treats which we have in the freezer also. When we freeze the chickens individually and pull it out to make a single meal you end up with a rather small quantity of bones each time, you would either need to store it until you have enough to make it worth processing or throw it away, which to me would be a waste.
With it just being DH and I the majority of the time we only need 12 to 16 oz of meat for a meal, this is about a pint size jar, so serving size wise it means fewer left overs.
There are times you just can't beat pulling out a bag of legs/thighs and making a good old pot of chicken and dumplings, or a roast of whole breast baked in a bed of home made stuffing (dinner last night, actually) but having the variety options available with the canning just means chicken can be used even more often than it was before.