Well technicaly shooting someone is a crime in many states and self defense is merely a legal defense against commiting the crime. For example justifiable homicide is still homicide, which is a crime that has merely become justified under the circumstances. The required elements present in those circumstances to be a justifiable crime vary from state to state.
Personaly I would not sue unless I sustained significant financial loss. Civil court is very different from criminal court and a "preponderance of the evidence" far easier to arrive at than "beyond a reasonable doubt". You could be justified in shooting them, but find yourself still losing in a counter suit over medical bills or some other claim regarding thier own financial loss from the situation. Losses they really did clearly incur with the only question being whether you are responsible.
Some courts could even declare that while the criminal was 90% responsible for the incident, you were 10% responsible and therefor 10% of the financial burden (of possibly hundreds of thousands in medical bills) is on you. Judges and jury members are individuals and there is some with very different views.
Even if you have an 80% chance of not losing in a counter suit, is a 20% chance of losing tens or hundreds of thousands from the counter suit worth gaining a few thousand from your minimal losses?
Now if they sue you, then feel free to counter sue them for losses. Otherwise let it go.
There is some states on the other hand that forbid the criminal from suing under statute for losses sustained during a crime. I guess in those situations only one side can legaly sue? Maybe it would be worth considering then.
Might as well put the tort system to some good use, if you ever get the chance then go for it.
Clearly someone lucky enough to have limited experience with the court system.
In court outside of TV and massive judgments that make the news there is few winners in big cases. There is just losers and bigger losers. Especialy in lengthy cases.
You could win $10,000 and still have legal bills totaling several times as much, nevermind the loss of time and energy, while the criminal already sitting in prison is losing no time coming to court to fight it.
The court system can be used to punish people. If you don't mind losing some to make someone else lose more that is fine, but expecting to actualy win more than you spend is excessively hopeful. Especialy if the person you are suing is a criminal with few personal assets, who is going to be in prison for some time earning no wages, and when he gets out likely won't make enough to pay you back before inflation has cut any settlement into a mere fraction of the value if they ever do. Even being awarded a judgement is only the first step towards actualy receiving the money. It can take years to collect, if you ever even do from a career criminal that spends much of thier life in and out of prison not working.
You on the other hand as a productive member of society probably have a lot more in assets to lose in a countersuit and certainly a larger income than the $0 the criminal in prison will be earning in prison, and will be expected and legaly forced to pay it in a reasonable amount of time.