Pretty much every rifle cartridge shoots faster in a longer barrel (with in reason). Going from a 20" down to a 12" barrel will give significantly less velocity. Small cartridges like the 5.56 rely on speed to give performance. Shorter barrels mean less speed. Larger diameter bullets like the 6.5 SPC rely less on speed and more on mass. Every cartridge is a compromise between bullet weight, velocity, portability, and shootablility. A .50 BMG has high bullet weight, high velocity, terrible portabilty and shootablility. The .22 short has low buellet weight, low velocity, high portability and shootablility. Everything in between is a compromise.
The 5.56 in its military configuration relies heavily on velocity for its wounding capability. Shorter barrels do not give the kind of results that longer barrels do. Since we are not military members (for the most part) bound to international law, we can use expanding or frangible bullets that rely less on velocity because the bullet will expand and do the work for us.
IMHO, there is nothing wrong with a .223/5.56 for defensive purposes as the range of bullet weights and construction allows for one to tailor the ammo to the mission.
The 6.8 SPC is heavier, slower, similar in portability and shootability. One deciding factor may be ammunition cost and availability.