We had rifle and shotgun zones here in NY, they have gotten rid of most of the shotgun zones including my area. I don't see much of a difference in harvest numbers but it is difficult to discern if it is because overall hunter numbers are dropping. We have, and always have had, 1 or 2 deer season human fatalities (including treestand fall deaths), and those are usually during gun season, but it hasn't gotten better or worse since rifles took over most of NY.
In my opinion laws should allow the hunter to use the weapon he is most comfortable/accurate with for the sake of the game they pursue. In general rifles are more accurate than shotguns especially past 100 yards. I would think places with open ranges and huge AG fields would view this topic differently but I don't think it is a stretch to say that most hunters wouldn't take long shots they aren't comfortable with. Of course there are some I can think of that "throw lead" at deer too far away but they are the exception to the rule, not the general rule. A deer in a common 3X9 scope looks like a dot at 400 yards and at that point you aren't able to aim at the heart/lung area and most people wouldn't even pull the trigger unless they are set up differently for long distance shooting. People that invest in a gun like that, tend to be the type that wouldn't shoot just to try and hit the deer.