Yes, there is a big difference. There are also a lot of other factors that figure in to the quality of wild meat, and I am disregarding all facts about killing and butchering.
I grew up in the bush hinterlands of N-E Saskatchewan and lived on wild meat, mostly elk, to start with, some moose, then later the whitetail deer (jumpers) became plentiful.
Then, as an adult I moved to Central BC and very shortly shot a nice fat, mule deer buck, before the rutting season. I couldn't believe how poor the meat was, compared to the Sask "jumpers". You are in Manitoba, so I presume your game would be similar to Saskatchewan game. With the whitetail deer in Saskatchewan we just loved the rib roasts. No wild taste, whatsoever. The last Sask whitetail we had was a large buck, actually shot in the rutting season, and it was still good meat.
My Dad was a good cattleman and he always said that the best beef came from an animal that had become thin over winter, then in the spring was fed all the chop and good hay it could eat, until it fattened right up, then butcher it. And he was right, this makes for tremendously good meat. I'll give away a secret here, a young cow that has had one calf, then not rebred, but given this thin then fast fattening, is the best beef one could ever hope to have!
I think the same is true of wild meat. In a cold country with long, hard winters and short summers, the game is thin in the spring, then have only a short summer to lay on fat, lots of fat, for the long winter ahead.
The game shot in rather cold areas, like all of northern Canada, including northern BC, is far superior in meat quality, to game shot in warmer climates, like southern BC.
I shot a large bull moose the first week in September in northern BC. The fat was marbled through the meat, especially the back straps, and one could eat that fat, just like you would with choice beef. In fact, it was hard to distinguish from good beef. I have stated before on these threads that I have eaten moose shot in late February in northern BC and it was still excellent meat.
No moose from southern BC is like that.
The elk also, from Saskatchewan and Alberta are far superior to the elk of southern BC. I have had them both and there is no comparison in meat quality.
It's complicated, but without a doubt, geographical location is a great factor in the quality of wild meat.