As far as FX goes, the difference is the slug liners have a faster twist rate and less aggressive choke, and sized at .217 ID.
For instance, the pellet liner was 1:21 and my slug liner is 1:16. The faster twist rate is needed to stabilize the slug, which is definitely a spin-stablized projectile compared to the drag-stabilized diablolo pellet.
Compare that to my Air Arms rifle at 1:17, you can see why it shot slugs reasonably well where my Crown with pellet liner did not.
I can't speak to the Brocock or Daystate rifles, but I've read that they shoot slugs reasonably well they way them come out of the box.