You are really talking about 3(and a half) major factors here:
1) Oil temperature: By allowing the damping fluid to be pumped external to the main damper piston you can reject more heat, this helps the shock fluid stay cooler and maintain a more constant viscosity and hence damping co-efficient. Having more oil volume helps in this respect too
2)Generally, the larger volume of the system also allows the designer to better compensate for changes in system volume through the travel range. Because the piston rods are single sided (generally) as the shock compresses, this rod “takes up” volume in the shock. This means you need somewhere to allow for that expansion. Piggy back canisters allow you to have a nice large nitrogen chamber behind a diaphram or second piston, that can absorb that volume change without an excessive pressure change (PV = nRT), again maintaining consistence of the damping co-efficient throughout the whole shock length
3) A remote reservoir opens up possibilities for “twin tube” design, where the fluid flow is in one direction only, and as such allows better use of the control orifices and crucially, tends to automatically bleed any cavitated fluid out of the primary damping stacks. Again, we are talking about consitence of the damping co-efficient at the full range of damper rod velocities
3.5) (The “Half point) Generally, a larger physical volume shock allows the designer more freedom to orient, mount and design the oil flow paths through all the damping elements. This results in less cavitation, less fluid power losses (effectively sticktion) and wider, yet more linear control authority (from the various damping orifice control knobs)
Simples!
(the downsides are that cost, weight and size all increase compared to a more conventional damper…..)