In the U.S., the founders expressly rejected the idea that courts and judges might bind the hands of the President and Congress in matters of foreign policy and security. The judicial branch is, by design, a domestic institution. When acting abroad, the American President, advised by Congress, retains all the powers that are inherent in an independent sovereignty. And that includes killing outsiders who pose a security threat. Sovereign nations have always had that power, and I doubt there are any that would explicitly disclaim that power.
Clearly, though, the powers the President can project domestically are circumscribed by the Constitution and can be reviewed by the courts. The touchy part is figuring out how to draw the lines: where does the jurisdiction of the court end and the sovereign foreign-affairs authority of the President begin? It is very dangerous to draw the line in a place that overextends the courts' inherently domestic authority and jurisdiction.
I propose that it's better to kill a terrorist like Al Awalki by drone strike than to degrade the judicial system by trying him in abstentia. Trials in abstentia degenerate to farce, and are illegal under federal law (http://www.slate.com/articles/news_and_politics/explainer/20...) as well as under the laws governing the International Criminal Court. Nothing in the Constitution says that due process always requires a trial. Saying that Al Awalki has due process rights, and that those rights are satisfied in his peculiar circumstances by consideration of an executive tribunal, does less violence to the rule of law than trying him in abstentia.