In 2010, a UK court ruled that Assange should be extradited to Sweden to face rape and sexual assault charges. One of the allegations has since been dropped. Prosecutors concluded that "at this point, all possibilities to conduct the investigation are exhausted." The statute of limitations expired on the other sexual assault allegation.
The cases against him in Sweden have been dropped or expired under Sweden's statute of limitations laws.  Therefore, the original extradition request no longer applies. In order for him to be extradited, Swedish authorities would have to reopen the case and reissue an extradition request. Even if they did this, given the request would have come after the US indictment, the US cases would likely take precedent.
The charges were only dropped on a technicality because prosecutors were unable to formally notify him of the criminal allegations against him. It was not because the victim changed her mind, or because the prosecution did not find the claims credible. As a result, when announcing the decision to drop the case in 2017, the Swedish Director of Public Prosecutions Marianne Ny deliberately reminded the public that she would be able to reopen the case as soon as Assange " makes himself available." Now he has left the embassy and is in custody in Britain, the Swedish authorities could very easily notify him of the allegations against him. They have already received a request to reopen the case and will likely do so. The Swedish case was opened before the US case. Therefore, it should take precedent should Swedish prosecutors decide to reopen it.
[P1] Assange's case was dropped in Sweden. [P2] Therefore, he has no charges to face in Sweden. [P3] Therefore, he should not be extradited to Sweden.
[Rejecting P1] It was dropped on a technicality. It will likely be reopened. [Rejecting P2] There are still credible allegations against him that he should face. [Rejecting P3] Therefore, he should be extradited to Sweden.