FN heavy cast bullets do a wonderful job of hammering game of any size. The appeal with modern cartridges is trajectory (real or imagined), less recoil (most of the time), lots of widgits and tech to debate over, way less wind drift at longer distances. Big one is we just open the box and play.
I have been mucking with a 45LC out of a Win Trapper. The 325gr FN GC are made from water quenched wheel weights. Very simple and dirt cheap to make. I launch them at 1550fps. At ranges out to 150yds, hitting with open sights is no problem (actually very accurate considering). I would feel confident in dropping all manner of grass eater out to 200yds. Trajectory is going to be steep and sights so so. However, put on a scope with a way to adjust for drop and voila, no different then shooting at 500yds with a 7RM. Recoil in this small light compact rifle is less then a '06 in a standard hunting rifle. For a woods rifle, this is ideal.
The hitting power of this slug is very impressive even by magnum standards and this is a small case/light bullet.
Move up to the 400 to 500gr and a larger case and you have a sledgehammer. Recoil moves up to big magnum levels so for those brave of shoulder, no big deal. Again, out to 250yds, trajectory is really not all that bad. This combo is routinely used out to 500m by BPCR shooters and black powder. With smokeless, you could go further/hit way harder.
I have seen what a 500gr 45 cal RN with a muzzle velocity under 1200fps does at 550yds on a dirt bank (this combo helped to destroy alot of buffalo). It moves alot of dirt. Moving that up to 1700 or 1800fps and you have a cannon. African monster stoppers is 500gr at 2300fps for comparison.
This has no comparison to a slug gun. A soft lead slug from a 12ga doesn't have the penetration potential of a 45 cal slug. Plus the accuracy of a SG is much less then a big bore rifle.
As a moderate range hunting rifle, it has been suggested that a 357 with heavy for cartridge cast FN is equal to the 30-30, the 44mag equal to the 30-06, the 45LC equal to the 300WM. Move up to the smokeless 444, 45-70 and now 450Hornady and you are playing with horsepower.
Jerry