To make a fair comparison, I think it is better to compare LS-C or LS-D to SS-D because that shows the building loads.

The conventional answer to how they differ is "LS-C has no ventilation loads", and that often makes up the bulk of the difference.

However, the two reports are calculated differently and equipment sizing would be more appropriate using the SS-D (or SS-J). 

The LS-D Report Building Load

• Based on steady state calculations (steady state meaning it assumes the whole building is operating at its design setpoints at the design hour and the hour before and so on)
• Does not include ventilation
• Does not account for building mass (because of steady state)

The SS-D report Building Load

• Includes ventilation
• Accounts for hourly changes based on the schedule. So if a building cooling setpoint was 85 over night and set to 75 the next morning at 8 am, there would be a load spike due to the rapid shift in temperature given the mass effects of the building
• Includes heat transfer across interior walls, floors, and ceilings (so if an adjacent room is not at the design setpoint, then the heat transfer will be calculated based on the actual space temperatures for that hour)
• Includes all loads seen by the coil such as fan heat, duct heat transfer, and even economizer effects.