How does doing a PhD with a pre-determined project vs. formulating your own affect your later career?
By selecting route one you are taking advantage of the potential that as your supervisor is more knowledgable of the field and so will know:


What the important/fundable/publishable problems in the field are.
Be able to judge if a project is likely to be successful
If a problem presents the correct amount of challenge to a graduate student. 


Thus if you choose option one, your project could be more likely to be successful and produce publications and lead to fundable options in the future. This does of course rely on the supervisor actaully being better at these things than you. While not all supervisors will be (or will care enough to think about them), on average this will be true.

On the other hand, if you choose route 2, then you will be able to demonstrate independence and initiative, which are highly valued attributes in the postdoc job market. A stock postdoc interview question, at least for me, is: "Name a situation where you had an idea independently of your supervisor and followed this idea through to its conclusion".