is a .223 barrel more accurate then a 5.56 NATO?

General Firearms Terminal Ballistic Information
1

is a .223 barrel more accurate then a 5.56 NATO?
just wondering because I am doing my first ar-15 build and I’m thinking about getting a DSA ZM4 upper and they are in 5.56 NATO

2

Barrels can be identical…the chambers are different.

3

Unless you’re planning on shooting long range matches, you wouldn’t notice a difference.