Tough question. Overall I prefer the TB. The blade seems like the perfect thickness to me. I also really like the blade shape better, the swedge, saber grind and thumb notch/rest all get high marks from me. Aesthetically it's a cooler/more aggressive knife...which I like.
However, I do prefer the ASH's handle. The palm swells fit perfectly in my large hands. Also, may hand fits nice and securely between the front guard and rear talon hole.
I love them both but if I could have only one I'd chose the TB.