As I haven't actually been out hunting and have only read opinions, I would have to say my viewpoint would be coming from an ethical and researched stand point.
First, I would rather an overkill instead of an underkill. no use in making an animal suffer for its death.
Second, wasted meat in my opinion removes some of the factor for killing the animal....resulting in overkill...the animal has died for your reasons, the least you can do is effectively use it to your means.
For deer I myself would like to use my 250 savage but due to area constraints I will be forced to use a shotgun. I am still researching whether to use buckshot or slug.
For moose I have a 303 british or a 308 win, which I hear both should be adequate.
If rifles were allowed in my area, would I use my 303/308 on deer? Why bother, my 250 has virtually no recoil and is my favorite and most comfortable rifle to shoot with. If I only had a 303/308 then I would research into the different cartridges available and use the most optimal one (in this situation I hear the 150gr for 308)