Ok, here are the results:
Whipping barracks wins 7 culture (barracks built T64 vs T71), but loses by 4 food, 5 hammers and 1 worker turn (finished T73 vs 72). Getting cows earlier online surely helps to catch those 9 foodhammers as working cow instead of rice nets +2 foodhammers per turn. Working cow instead of copper is probably roughly in the same ball park, but the effect comes of course through earlier city growth.
Additional variables:
- With later barracks we have more worker force in hand when we pasture the cow and the real difference between worked cow turns is either 5 or 6 turns
- Our workers have also other valuable tasks to do during the turns 72-77 as they chop us a settler in Agincourt, granary in Dunkirk and barracks + granary in City E.
- Remaining at size 2 enables an emergency bowman-whip
All in all, this is a really really close decision. I'm still leaning towards remaining at size 2 because of aforementioned reasons, because I'm biased towards my own sims
and because I need to go to sleep! I hope you are not too pissed off by this! 
I promise that if this is a wrong decision the margin is very small!
PS. You're welcome lurkers. This was surely again super-duper interesting. for you too.
Whipping barracks wins 7 culture (barracks built T64 vs T71), but loses by 4 food, 5 hammers and 1 worker turn (finished T73 vs 72). Getting cows earlier online surely helps to catch those 9 foodhammers as working cow instead of rice nets +2 foodhammers per turn. Working cow instead of copper is probably roughly in the same ball park, but the effect comes of course through earlier city growth.
Additional variables:
- With later barracks we have more worker force in hand when we pasture the cow and the real difference between worked cow turns is either 5 or 6 turns
- Our workers have also other valuable tasks to do during the turns 72-77 as they chop us a settler in Agincourt, granary in Dunkirk and barracks + granary in City E.
- Remaining at size 2 enables an emergency bowman-whip
All in all, this is a really really close decision. I'm still leaning towards remaining at size 2 because of aforementioned reasons, because I'm biased towards my own sims
and because I need to go to sleep! I hope you are not too pissed off by this! I promise that if this is a wrong decision the margin is very small!PS. You're welcome lurkers. This was surely again super-duper interesting.
for you too.