It definitely makes a difference to can office chair if you are able to adjust the headrest. The main difference being that you can customize the chair even further to suit your head, neck and accommodate for any neck pain you may have.
Some of the chairs on our top five list have headrests that only allow you to adjust the height. But some give you the ability to adjust the tilt of the headrest too, which allows you to get the absolute perfect position to aid your persistent neck pain.