I have a Combat Unit Railgun...handled a bunch of Clapps but never shot one. I would expect them to all function the same.
Pete Single did the checkering on the Clapp guns; they'll be a little different visually from the factory checkered CCU guns, but function will be the same.
The Combat Unit guns are all S80/have Colt's firing pin safety; the Clapp guns are all standard fire control (what people keep calling S70, but Series 70 indicated a collet bushing and "accurizer" barrel; it had nothing to do with the fire control setup..)
For me, as my CCU gets carried on occasion, the Series 80 stuff is fine. It really does not impact your trigger; Colt ironed all those issues out right after introduction. I prefer a S80 gun over the USGI gun setups, but YMMV.
The sights on the Combat Units are full black rears and a nightsight front; on the Clapp guns, it's a brass bead front, same all black rear. The brass bead isn't BAD per-se, but it dulls easily; you need to keep wiping/polishing it. A true gold bead would work better, but they're also pricier.
The Clapp guns have a standard blued finish which is great; the Combat Unit guns are all ionbonded grey. It's not bad, but it's kind of utiltiarian. I think the Clapp guns are all carbon steel (except the stainless ones of course); all the Combat Unit guns are iirc stainless under the ionbond.
Also, I prefer the larger thumb safety on the Combat Unit, though honestly both the safety on the Clapp and on the Combat Unit would be getting swapped out for a Wilson or Novak thumb safety, for me. The un-dehorned rear edge of the factory Colt safeties eats the web of my thumb terribly; the Wilson is much nicer for me in that regard.
Honestly, it's %95 visual stuff; there's no real mechanical difference between them. If you prefer Pete's checkering over Colt's factory checkering, go for the Clapp guns; if you want something that looks a little more industrial that you wouldn't cry if it gets a scratch on it, go with the Combat Unit.