Is a 9mm bullet more accurate then 223 caliber bullet?

Generally, a bullet's caliber has NOTHING to do with its accuracy.

So your question cannot be answered.

However, a 9mm is usually a handgun round, used at close range (0-15meters). A .223 is typically used at longer ranges, but could be used close-up as well.

At distances greater than 20 meters, up to 500 meters, the .223 will be more accurate, if the weapon is dialed-in.