Whoa ... new life for a thread almost a year and a half old ...
TDA stands for Traditional Double Action, which in a semiauto pistol usually means that the first shot is fired with a double action trigger stroke and the subsequent shots are fired with a single action trigger stroke (fired from the hammer-cocked condition).
As far as why I prefer the CS9 to the CS45?
It primarily has to do with the way the CS9's grip profile fits my hand much better than the CS45's, and the controllability of the 9mm cartridge in the CS9 offers me a noticeable advantage compared to shooting .45 ACP in the CS45.
Also, like some of the other diminutive .45 ACP platforms out there, I've always thought that the CS45 still demands a lot more of the shooter than the larger size platforms.
Stuffing a big cartridge into a small package can introduce some potential for functioning issues unless everything happens just right. Decreased slide mass & slide travel, increased felt recoil & slide velocity ... and then you have a large diameter cartridge that has to be stripped from the magazine lips, fed & chambered during the shorter and faster forward portion of the slide's movement. For me, the CS45 slide typically snaps forward into battery with just the slightest hesitation, sort of a 'ka-thunk' (which becomes more pronounced as the recoil spring becomes worn), while the CS9 snaps into battery with an abrupt 'thunk'. I guess I could describe both models as 'brisk' when it comes to returning to battery, but the CS45 is just a bit less so ...
I can 'break' the angle of my wrist support and/or relax my grip and sometimes induce a 'limp-wrist' malfunction with the CS45. I haven't had the same experience with the CS9.
FWIW, I've found the slightly larger 457/4513TSW platform to be more 'forgiving' than the CS45 in this regard.
If I had to choose between my CS45 and my 4513TSW, keeping only one of them, I'd choose the 4513TSW (or a 457S).
As it is, I'll keep trying to wear out my CS45 before I think about getting rid of it. I just carry the CS9 much more often.
Still don't claim to have 'the answers', though.