In Texas, a Citizen's Arrest is legal under the described circumstances.
If you see that a person is armed, and he runs away, Texas Law states that deadly force may be used if the fleeing person can be considered a threat to others of the community. Shooting such a person in the back is legal. Granted, you may have a certain amount of difficulty proving your case, but that's an issue of credibility, not the law itself.
At any rate, if your are certain of your capabilities, there is no reason not to take the person in custody for the police.