The typical criminal considers himself (maybe I’m being sexist, but the vast majority of violent criminals are male) successful if he gets away, regardless of whether he accomplishes possession of whatever it is he is trying to steal. If you successfully stop a theft (for instance, you managed to pull a gun, and you end up not having to shoot), and try to do something stupid like a “citizen’s arrest”, then the perp’s thoughts will become completely focused on getting away. You can count on some of the things he will consider doing will involve hurting you.
I make it a point to mention in my CHL classes that citizen’s arrest is almost always a bad idea, for many reasons.
In such a case, it is usually better for you to allow the low-life to leave. You can (and should, especially if you have drawn a gun) call the police, and describe the criminal to the best of your ability. If you managed to get a photo of the perp, that’s even better. By allowing the perp to leave, you significantly reduce your chances of being hurt or killed.
Another version of this is the case where you stopped a mugging using a less-lethal defense device such as OC spray (I’m not a big believer in OC spray, but I will admit that it can be useful under some circumstances), and the attacker is temporarily incapacitated. Then it’s time for you to leave. Whether you leave, or the perp leaves, you have increased the distance between you and the criminal, thereby increasing your personal safety.