Basically, a Champ runs 140 STR. So generally, a TTHH would be better.
However, if you don't have celebs and can only get about 130, a THHS would be better. A TTHS would be a bit of a waste, unless you plan to MvP with it, but a AAAT Mace is better for that.
And to add to that, a THHS might actually have better FO damage, since its multiplier isn't as big as Asura is.
So you decide, either TTHH for maximum Asura firepower, or a THHS for mid-STR's and FO damage.