Mine would be my Uberti clone of a Winchester 1866, in .38 Special. It's got at least 30,000 rounds down the pipe, and probably triple or more that figure in dry cycles. The barrel is still stock, and will shoot a string of ten into a group a little bigger than a quarter at fifty yards. The action's been rebuilt a couple of times, but more to keep up with advances in gunsmithing than because it was worn.
I've never reached that high in round count in cowboy pistols, partly because the 60 rounds a match is split between two guns, and partly because I've been through several sets in the time I've shot that one rifle.
Next highest would likely be my Taurus PT1911, which was originally my CCW piece, and has since morphed into a USPSA Single Stack gun. It's probably around 15,000. It had a good deal of trouble with small parts breakages at the beginning, but has been solid for some time now.