I was going to reply back to you over on the other thread that you brought this up on. AA accounts for ~30% of your total damage. So the 7 Str and fairly heft Crit that you lose to gain a relatively small amount of Det (by comparison to what you lose) would net you a noticeable DPS loss. It will be extremely rare when sacrificing raw Str is going to be the way to go generally speaking.
Also is the set you are comparing your purposed set against? http://ffxiv.ariyala.com/LRGE
Edit - Grabbed the wrong link. Had the one for no ACC requirements. Whoops, but it's fixed now.
Edit again - I see that is not the set you were comparing against. So with the setup you posted on the other thread compared to what I linked above which is what many of us are shooting for now the difference between the two would would be -7 Str, -25 Crit, and +15 Det. I couldn't advise that switch to anyone.