I decided to look that up.
Both rounds with Hornady 40 gr. Vmax
223:
Muzzle- 3800 fps, 1282 ft/bls, -1.5"
100- 3249 fps, 937 ft/lbs, .9"
200- 2762 fps, 677 ft/lbs, 0"
300- 2324 fps, 479 ft/lbs, -5.5"
400- 1928 fps, 330 ft/lbs, -17.6"
500- 1578 fps, 221 ft/lbs, -39.1"
204:
Muzzle- 3900 fps, 1351 ft/lbs, -1.5"
100- 3482 fps, 1077 ft/1bs, .7"
200- 3103 fps, 855 ft/lbs, 0"
300- 2755 fps, 674 ft/lbs, -4.3"
400- 2433 fps, 526 ft/lbs, -13.2"
500- 2133 fps, 404 ft/lbs, -28.1"
The 204 retains energy and velocity better due to a higher BC (smaller diameter, same weight, same design bullet). The 204 is legal to hunt deer and antelope with in Nebraska because it has >1000 ft/lbs at 100 yards and does work (but I'm sure someone has successfully done it with the 223 here or elsewhere too). There is less drop at all yardages too.
The 204 does have the option of going faster and flatter with lighter bullets and the 223 doesn't offer that. The 223 does offer the ability to shoot heavier bullets but this is better done with one of it's big brothers (aka 22-250 or 220 Swift). If you really want to compare the 204 to a 224 caliber cartridge then the 22-250 is a better comparison.