There's a pretty significant difference between your two examples. In the first, you are editing existing data and as such it makes sense that everything will just save in real time. In the second example, you may or may not create an entity. Here, cancel is really important. If I click the new contact button by mistake I do not want an empty contact to be created if I back out.
So the questions you need to ask yourself above all else as far as which button is appropriate;
Am I creating something or editing something that already exists?
If you are editing something that isn't new you probably want an arrow and to save immediately. If you're making a new thing, you need to have an obvious way to cancel doing so.
If a user backs out during entity creation, should that entity be created or discarded?
Unless you want whatever is on the page to be mandatory, you should give people a way to cancel that is very clear and also be as clear as possible that going back will destroy any entered data.