Shang Chi wins.
IMO he is the Marvel equivalent of Richard Dragon (the two are basically analogous), and in his mini-series RD managed to show that he was indeed a better combatant than Bronze Tiger.
Now, this is not to say that BT is not a great fighter (he is absolutely amazing), but he would probably find SC as tough an opponent as RD.
I'd have to say Shang Chi for the win.
Shang-Chi would take 5.5-6/10 without his chi capabilities, with his chi he is going to take close to a clean sweep. Shang is more skilled than Turner, he can amp his stats with chi and has a variety of quasi-mystical chi based attacks and defenses under his belt that place his offensive and defensive abilities on a much higher level than Turner could even dream of. Shang-Chi at his best isn't even in the same ball park as Bronze Tiger. It's about as fair as a roided out MLB player versus a public school little league pitcher.