Have you considered experimenting?
Get a dozen eggs that are the soy free etc eggs you are trying to emulate in your flock, and a dozen that are pasture raised.
Don't open the egg cartons to see the eggs.
Have a friend remove the labels- make one dozen "dozen A" and the other "dozen B" -- maybe the friend switches the eggs from one carton to the other, or to identical cartons - and only your friend knows which one is which.
Use one dozen and then the other and see if YOU notice any difference in how your body reacts to one over the other. Not the flavor - your own eggs will always taste better. I'm referring only to how you do physically.
I suggest this because going the soy-free etc. feed route is extremely expensive, and that's saying something given what we're paying for chicken food right now.
As
@U_Stormcrow was saying, it might not make any appreciable difference to you... So maybe find out while your chicks are young and as cheep (hahah) as they ever will be to feed.