Depends on the compound bow design. The older ones can be unstrung much like a recurve, but any vaguely modern compound requires a bow press and specialised gear. Meanwhile a medieval crossbow just needs a bastard string and whatever spanning mechanism it uses normally.
The compound bow's major advantage is that you can hold it at full draw with comparatively little effort, due to the way the cams have altered the force/draw curve. The permits longer time aiming, thus greater accuracy.
Other common compound bow accessories like release aids, allows for much greater consistency.
On a separate note, the limbs of a compound bow are very short, much like a horsebow. This means you're probably only going to manage a a two finger draw at most as the string angle will be too acute for a full draw, which limits the amount of power you can put it in (as you have less points of contact to draw the bow). Typically you'd get around the issue with a release aid, so that's another fiddly mechanism to add to the compound bow.
As Max said, D&D doesn't have the granularity to properly model the differences between bows in general, let alone a compound and a recurve (force/draw curves, being able to hold at full draw for longer, shorter bow lengths, string angles, etc) beyond giving it Masterwork status and a +1 to hit.