the question is:
Can Julian Assange and Wikileaks be charged, tried, convicted and sentenced for publishing classified material?
the answer is: No as this is actually settled case law.
The case: New York Times Co. v. United States
The issue: Can classified documents in the possession of a newspaper be
published?
The ruling: The USSC ruled in favor of the NYT and WaPo. The decision (6-3) in part stated:
In order to exercise prior restraint, the Government must show sufficient evidence that the publication would cause a “grave and irreparable” danger.
The Pentagon Papers and the Wikileak's documents are (probably) on par with each other and to convict Assange (and Wikileaks) the government would have to prove the "grave and irreparable" piece.
Plus there is the issue that Assange and Wikileaks did not publish these documents from within the USA so the State has no jurisdiction in Sweden where the alleged "crime" took place.
Please note PFC Bradley probably does not enjoy the same protection as he
(1) stole (not the right word but it's 5am in the morning and my brain isn't 100% yet) the documents in what could be considered espionage.
(2) acted inside the jurisdiction of the USA (a military or other federal facility in another country is considered
de facto and de jure, by both US law and international, law as US territory.