You have more leverage as a contractor I think, the position is different to an employee. Clauses like noncompetes and IP claims outside of the contract are a pretty hard sell for a contractor, as it limits your ability to work after the job is done and as such it's going to be hard to hire a contractor with those kinds terms. I imagine clauses like that are designed to keep employees around for as long as possible, not really an aim if you're hiring a contractor.
Depends on the goals of the contractor. They might concede to some crazy agreements to be able to list a big name company or a high profile project on their work history to get higher paying work in the future.