Barrel length and twist can come into play. Say a AR pistol w/7" barrel vs a AR rifle with 20" barrel. Or a 1/12 twist vs 1/7 barrel twist.
For .223 vs 5.56 the firearm chamber is the main difference (5.56 is made to cycle full auto and high sustained rates for the military).
The rounds for the most are based on the load, for example the .223 load was exactly the same as the 5.56 M193 that the US Military started out with with 55gr FMJ using a 1/14 to 1/12 twist. But, when FN developed the NATO 5.56 in 1972, as the SS109, the US came up with M855 ball, being a 62gr bullet green tip at higher pressure, and due to heavier tracers used a 1/7 twist. A 1/12 barrel will NOT stabilize a 62 gr round. a 1/9 twist is best for a 62gr round, a 1/6 is best for orange tip tracers (military did 1/7 to split the 62gr, and heavier orange tip tracer). 1/8 twist is seen as the best balance...
Military wise; The 55 gr in a 1/12 to 1/9 twist works well for its ability to tumble on impact, just like the Russian 5.45. The 55gr FMJ is the most lethal overall. The 62 gr green tip ice picks, and goes straight through, small holes and is not that effective. The Mk262 77gr was/is a boat tail hollow point, made for accuracy/long range, and now is called an Open Tip Match for political correctness... The 77 gr is the most accurate and sub MOA, around 0.80" at 100 yards capable (.77 MOA reported by some) and it causes slightly more injury as it separates and tumbles slightly. Then there is the M855A1 metal/copper tipped, that is long, not accurate, and causes a lot of wear and tare on M4/C8's, but its "lead free". There is also armor piercing M955 steel/tungsten tip/core that is legal, but highly regulated...
On the law enforcement side Gold Dot soft points are good and available in a few weights. 62gr is my choice. It expands and does good damage and does not ice pick. Similar to hunting rounds, but holds form well due to being bonded.
Then you have the nylon tips, that. I dont have much experience with, but are a hunting type ammo like the soft points and used in self defense loads.
Application is important with a small caliber centerfire like the .223/5.56. An 11.5" barrel is effective to 15 yards or so, a 16" barrel good to 100 yards, and 20" good to 200 yards (not accuracy, but effective 2000 to 2200 FPS on impact to cause a temporary wound cavity. Some ammo is good on heavy clothing, some good on barriers, etc. M855A1 is good for say use on a vehicle, soft/hard armor, vs M193 being good for ISIS wearing robes...