I've done some experimenting in the Training room using three Iron Assault I Heavy Bowgun (one with close range mod, one with long range mod, and one with no mods) to determine how the Close Range and Long Range Bowguns mods work.
The Close Range Mod increases damage if you're within just shy of 1 roll of the target, and the Long Rang Mod increases damage if you're just a little more than 2 rolls away from the target (you'll be outside the range of Normal Shot). Both shots seems to give the same damage boost, and appears to work on any shot which makes use of critical distance (i.e. shots like Slicing and Cluster don't benefit from the mod) including the the Wyvernheart special ammo (Wyvernsnipe doesn't appear to benefit from the mods).
So what this means is that if you're primarily going to be using Normal and Spread shots then you should use the Close Range Mod, and if you're going to be using a lot of Pierce shots then use the Long Range Mod.