[rcxdude]

I broadly agree that both are important, but I think the difference lies in the level to which the person feels about the two scenarios you post. Some people are far more upset about the former than the latter (and also consider what happens if you modulate it by the crime committed).

(And of course it's not a strict either/or as well: you can have a rules of engagement for such things. e.g. in the UK the police are not blanket banned from pursuing a fleeing vehicle, but they need to have had appropriate training and do so only in particular circumstances)