FOR ME, Longbeard is much better than Double X, although lots of turkeys were killed with Double X and everything else before LB came out. And I think you'll be surprised how much better #5s do than #6's. I've just never had the need or desire for the TSS, although no doubt about it's effectiveness. I don't like the cost, and so far, haven't needed it.
I haven't even killed a bird with LB, just XX, Federal Premium #4 and Remington Premier or Nitro Mags.
Possibly a few dove loads tossed in many moons ago.