Mietla, yes I would.
On a sidenote, the Europeans are not going to extradite if something that isn't acceptable happens to the dudes that is extradited when he is abroad.
In your example, something acceptable to your country (i.e imprisonment) happens. The two examples are therefore far from the same.
In the end, it's the country who holds the detainee who decides. Btw, this policy of not extraditing to the US unless there's a guarantee that there won't be a death penalty waiting for him is not new - it's been in place for many years.