Whats the difference where you put a scope on a round barrel unless your talking about indexing a barrel.
After purchasing a scope-mounted anti-cant level and properly mounting it, I can vouch that there can be big differences to be dealt with.
The first thing that I did was align my scope crosshairs up with a known level object to gravity, similar to a plum line, and then went ahead and mounted the level onto the scope to proper level with it.
I then cobbled together some level objects around my air rifle to get the stock and barrel as level as I possibly could confirm, which is when I noticed that I did indeed NOT mount my scope properly, it was canted about 3 or 4 degrees clockwise. I then picked my rifle up and shouldered it, and realized that [apparently] I have been in the habit of slightly canting my rifle as I hold it without realizing it.
In many situations I don't think that a slight cant would "break the bank," but it is an interesting learning experience, considering that I never really investigated the idea of this in my 3+ decades of shooting, even as a sniper. But it makes sense, when you take into account that most scopes are mounted almost 2" or more above the bore, and that the flight path of a pellet has considerable angle and arc in relation to line-of-sight with the view from the scope.
For instance, I have this particular air rifle sighted in to zero at 27 yards. But the center of the scope is about 2" above the center of the bore. So over the course of 27 yards (about 25 meters) of flight path, the pellet leaves the barrel at an upward angle, technically more upward than what the target is at 27 yards, but gravity starts arcing the trajectory downward at the moment it leaves the muzzle. So the pellet "falls" into the intended vertical POI in the crosshairs at that 27-yard distance. If the scope is canted left or right in relation to the bore, elevation adjustments on the turret (and a converse relation to windage as well) can become inaccurate because every click up/down on elevation will produce a slight deviation in windage as well, even if the windage turret is not touched. I wouldn't be so picky if it wasn't for the fact that the cheap air rifle that I bought is extremely accurate to begin with, so in regards to my luck with it, I am trying to squeeze the most accuracy out of it as possible.
An extreme.example would be if you sighted in an air rifle like this at 27 yards, but the entire rifle/scope was canted 90 degrees on it's side to the right, with the barrel being on the left, and the scope laying to the right. If you managed to zero it at 27 yards in this condition, you would find extreme deviation beyond that distance. At 50 yards, a simple "holdover" would not be effective, because the pellet would have drifted several inches to the right after it intersected the original sight-path/zero at 27 yards from left-to-right.
PT