It doesn't actually affect the decisions too much in these particular cases. The cases for and against extradition are invariably fought over issues of human rights, and the law is quite clear that British and EU statutes apply equally to everyone regardless of nationality, at least in considering most of these issues. While the person is in the UK/EU, the national governments cannot use their nationality to overrule any HR arguments against extradition, unless the law specifically prescribes a difference course of action based on nationality, which must not unduly remove any of their human rights.