We've gone over this before.

Compare the best 40 grain bullets in each caliber for BC (40 grain 22 caliber Ballistic Tips to 40 grain Vmax or even the 39 grain BlitzKing). Load them bother to similar pressures, in equal barrel lengths. The 223 will gain velocity when loaded to potential and not kept to 55K. It ends up so close as to be a wash, at the distances small varmints are normally shot with these bullets. The 204 comes out to like 1" less drift at 400 yards in a 10mph wind, which is meaningless when you're already aiming a foot and a half off a prairie dog for windage.

Practically speaking, they're same/same.

Some folks claim the 204 kicks less with similar bullet weights, allowing them to see hits through the scope versus a 223 shooting similar bullet weights, but I've never seen it.