It largely depends on the bullet's ballistic coefficient but also depends how long the bullet is being pushed by the wind and how strong the wind is. Meaning if you shot the same bullet at 2000fps then 4000fps, the faster one would have less drift over a given range compared to the slower one.
Use a ballistic calculator that accounts for wind to get a better idea on how wind will effect the bullet's flight.
In a 10mph 90 degree crosswind you're looking at about 1-2 inches of drift(with .223/5.56), depending on the bullet's BC. The higher the BC the less the wind will affect the bullet's flight, and on top of that, they will lose less velocity over a given range compared to a lower BC bullet. To give you an idea, a typical 9mm 124 grain bullet would have close to half a foot of wind drift, in the same conditions.
but how different is it for .223/5.56?
.223 drifts significantly less than .22LR because you're generally shooting spizters in the .223 and round nose in the .22LR. This gives the .223 higher BC bullets, in general. It also gets shot at roughly 3x the velocity. So less time of flight to the target means less time in the wind. At 100 yards .223 has roughly .1 seconds time of flight. .22LR takes .32 seconds to reach that same 100 yard mark. That being said, .224 cal bullets generally don't have incredibly high BC bullets... Not when you compare them to heavy 6.5mm, 6.8mm, 7mm, .308, .338, .50 cal projectiles at least. So they can get pushed around in the wind a bit. No where near as bad as .22LR, though.