I tried seeing your other post, but for some reason I was not able to view it.
In any event, the .223 is generally an accurate round. Similarly, Tikkas are generally accurate rifles. Therefore, putting the two together, I would say that a .223 in a Tikka should make for a real tack driver.
Coincidentally, a friend of mind had a Tikka Varmint in .223 and it shot incredible 1/4" groups with federal match grade ammo. I wanted to buy one very badly, but the best deal I found was in a .22-250, and I only wanted a .223.
I'm sure that a .223 in a T3 will also be accurate, but the Varmint version should be more inherently accurate because of the heavy barrel.
In any event, I think that you can't go wrong with the .223 in the T3.
Zachary