Which is the better choice, and why?
I generally hear "under contract" as an adjective and "contracted" as past-tense verb:
The person/organization performing the activity is "under contract" and the person/organization requesting the activity "contracted" to have it done.
You can say "a network of doctors and hospitals under contract to provide services", or "the local authority will contract with a wide range of agencies to provide services".
"Person P is/was under contract with organisation O to do job J."
"Organization O (has) contracted person P to do job J."
Which do you want to emphasize, the person who took the contract or the organisation that gave it out?