I would say it depends on the specifc circumstance. If the deer were shot and injured badly by the first hunter and would probably expire within a day or so I would say it should go to the first hunter, as long as that first hunter were trying to make a recovering etc. Anymore than that and I would say it is the person who puts the final kill shot on it.
In the case of your bear, that is tough to say. Sounds like you where gone and out of the area. Had your uncle not been out looking/hunting the bear probalby would not have been found. It had survived for a couple days. He put the final touch on it. But still, sounds like it was pretty dead when he came upon. Tough to say.