Interesting situation.
You have a veteran QB with a pedigree background with a Heisman and a BCS championship who was off an on in his starting career in the NFL.
On the other hand you have a gadget player who really didn't prove himself as a QB at the college level, and is just 6/13 throwing the ball in the NFL.
If they start Winston, they know what they might get -- a guy who can toss the ball and fit into the pocket passing offense Brees runs but may, given inaccuracies, not be able to deliver the wins like Brees.
If they start Hill, they may have to install a bit of a new offense to take advantage of his ability to run, run RPOs, and other packages the offense only knows from the playbooks as opposed to rolling out in actual games.
In my mind, going with Winston is a much surer proposition, and I don't have a high regard for Hill outside of a gadget. But can see the argument as to why they would want to give Hill a shot after having him sit behind Brees this long.