Generally a country will only extradite you if the crime alleged is also a crime in that country. Some countries also stipulate that the punishment must not be severely stronger than in the current country.
Generally that's the case. However, Sweden was trying to extradite him under a European Arrest Warrant which has no such requirement for the offence to be a crime in the country being extradited from and has much weaker safeguards in general. (This has caused some problems over the years.)