I own an 'original' (6-shot mag) 4513TSW and a CS45S (stainless slide). I bought both when they were still new models and have fired them a fair amount (I've lost count of the times I've replaced recoil springs in both).
Overall, while the CS45 is a dandy little TDA .45 pistol, I'd think the 4513TSW (and its 457/457S variation) might be a more attractive choice for some folks.
It's not an uncommon phenomena for the smallest .45 pistols to often be reported as being less tolerant of shooter & ammunition issues (especially relating to shooter grip technique offering anything less than a firm grip and locked wrist for frame support during cycling).
Also, as the slide run distance (travel) shrinks in increasingly smaller & shorter .45's, there may be some 'feeding/timing' issues arise when not only less-than-optimal shooter grip techniques are involved, but either lower or higher powered loads are introduced (like 'budget' loads on the lower end of the normal power range, or +P loads which slam the slides back with more snap).
Something else which might be a consideration is that the CS45 uses a 6-rd mag dedicated to it alone (a second set of indentations pressed into the mag walls to help prevent the displacement of the top round under the harsher recoil developed in the little gun), while the mags used in the old/current 4513TSW's (6 & 7-rd), as well as the 457's (7-rd) & the 4566/4506 (8-rd) mags just require the standard P-lip indentations. Due to the number of current style 4513TSW's & 457's produced, the 7-rd mags are probably going to be easier to find than the CS45 mags, on any given day (although all can be ordered through the factory).
The 4513TSW/457's can be used with stock grips or Hogue rubber stocks, but the CS45 only came with a set of special Hogue stocks made for the gun. The factory's reasoning (I was told) was that customers liked the aftermarket Hogue grips on other guns, and the extra cushioning of the short rubber grips made the recoil feel more manageable in the harder kicking Chief's Special pistols. personally, I find the CS45 grips to be a bit thick & chunky for my medium-size hands, but the CS9 grips feel like my hands had been used for the mold. Suit yourself.
I had Hogues on my issued current production 4513TSW, and after spending a couple of years shooting my 4513TSW in all kinds of weather, and having the stock grips be a bit slippery under the increased recoil of +P loads (when I was trying them as an alternative load), as well as when my hands and the grips were wet, I modified a set of Hogue grip stocks to fit the cutaway profile of my 4513TSW. They remain on there to this day.
Each potential owner will have to decide which model best suits their own experience, skillset and desires, though.
4513TSW old-style & CS45 (I'm posting thumbnail links to decent size images because the full-size pictures were HUGE when posted).
Old style 4513TSW with current production version:
The only thing that bugs me a bit about the current version is the separate accessory (light) rail. I don't use them, myself, but if I did, I'd prefer they'd have incorporated the rail into the frame like they did on the 4566TSW (and the full-size 9/.40's). I've seen a couple of the rails experience breakage on working guns which required replacement. I think if I had it happen to a personally-owned 4513TSW, I'd ask them to simply remove the broken rail and fill the dustcover holes with rivets, leaving the rail off. That's just me, though.
It's weird, but the CS45 was one of those guns which I really wasn't all that enthused about having bought for the first year or so. The 4513TSW was simply an "easier" gun to shoot. Better recoil management & controllability. The size of the CS45, while smaller in a couple of dimensions, wasn't really all
that much smaller once you factored in the belt holster, too.
Day in & day out, I suspect the 457/457S/4513TSW might be a better choice for all-around use and a lot of shooting than the CS45 for a lot of folks. Maybe. Dunno. Not really my business.
I've run a lot more rounds through my CS45 than I have my personal 4513TSW, but looking back at it, I tend to feel that was because I was working harder to master the smaller CS45 with the chunky grip profile and the slightly increased felt recoil (muzzle snap/whip). (Also, why beat up my own 4513TSW when I can use & abuse the issued one?

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Best thing I could suggest is to try and find examples of both to shoot before deciding ... or do what i did and buy both, and then go back and forth about which one you like better for many years ... while keeping both. Dunno.
Good luck.
