The main difference in the cases is that the 5.56 brass is thicker, and so uses less powder to create the same pressures. So if you're loading 223 brass, you can certainly use 5.56 loading data and work up from there for hotter loads. But if you're loading 5.56 brass, using 223 data will create too hot of a load to begin with. Stick with the data for the 5.56 to begin loading that brass.
This is all wrong. Beside the fact that you have the case capacity backwards, 5.56 load data runs at a higher pressure than 223 data. 5.56 data is few and far between, but it is available from Western Powders. Their 5.56 data runs at 62K psi while their 223 data runs at 55K psi.
Starting out with 62K 5.56 data in a 223 case(less capacity) in a 223 chambered rifle may not be such a good idea. Best to load for the specific chamber instead of the brass headstamp. Then you can determine case capacity and if you need to adjust accordingly.