I used to write for Singletracks, and a while back I had the chance to ride two rigid carbon MTB forks, one with a QR, one TA. Both forks from the same company, both the same geometry, same frame, wheels, tires, and trails. You can
read the whole post here, but in summary: for a rigid fork the QR axle is 95% as stiff as the TA. I could hardly tell any difference at all in how the two different forks felt while riding. And what little difference I could feel, it's hard to say if it was really the axle that caused it, because the forks were not identical, the TA fork had beefier blades, but the QR fork's crown looked more solid. And without knowing anything about the carbon layup, you can't even tell which one is stiffer just by looking at them anyways.
TA doesn't hurt, but it doesn't improve the experience on a rigid fork like it does on a suspension fork where it makes a HUGE difference.
The TA set up was heavier and more expensive.
You can always use a thru-bolt, that very nicely bridges the gap between QR and TA, and it works with any QR fork (though you need a compatible hub of course).