These are the two most famous players in the ongoing Wikileaks scandal, and there are calls to prosecute both, up to and including the most severe penalties available under the Espionage Act, and in fact, charging one or both with Treason.
Ex-PFC Bradley Manning, a US citizen and Private First Class in the US Army, is the alleged leaker of sensitive information to a foreign national (Julian Assange) who published the information far and wide. He is subject to US jurisdiction both by citizenship and by location of the alleged actions, and as a US citizen and member of the military owes a duty to both. By copying classified information and distributing it to non-authorized persons, in gross violation of duty owed, he committed crimes possibly rising to the Constitutionally-defined level of treason by “adhering to [the United States] enemies, [and] giving them aid…” (Art 3, Sec3 US Constitution). If he did these things, he is (IMHO) an honorless oathbreaking traitor. The US federal government has moral and legal claim on him, and therefore may prosecute him to the fullest extent.
Julian Assange, Australian citizen, sometime resident of Sweden is the admitted publisher of this sensitive material, and probably did so with the express desire to harm the interests of the United States. But he is not a US citizen or resident and is (and was at the time) not on US soil when the events took place; and owes no duty to the US. The US has no jurisdiction, and thus no ability to prosecute criminally his actions. The US can bar him from ever entering the US, or becoming a citizen. I suppose the US could declare war on him, but not charge him with a crime. He opposes the interests of the US, but acting against the interests of the US is neither a dishonorable action or a violation of trust for him. The US Government has no moral or legal claim on him, and may not prosecute him for anything.
Citizenship means something, as do borders, remember. Otherwise, why bother fighting illegal immigration and the efforts of the US and EU to undermine US sovereignty?