We have looked round both Headington and OHS. We also know people with kids at both. Both are great schools.
Oxford High is more academic, as you'll see if you delve into their stats. Back in the days when more academics could afford to live in north Oxford and send their children private, it was where Oxford dons sent their daughters, and this reputation for being academic still lingers. Headington does well and there are very able kids there, but when you look at the results, there is slightly more of a tail and a smaller proportion getting the absolutely top grades. It's extremely subjective whether that matters to you.
OHS used to have a reputation as a bit of a hot-house for this reason, but there is a lot more emphasis on pastoral care now and the current head seems really hot on this. (Responding to previous posts, our friends with kids at Headington have nothing bad to say about the pastoral care there either and describe it as a supportive school.)
Headington's facilities are undoubtedly better. OHS has good facilities but Headington's are extraordinary, especially for sport and art. And Headington takes sport very seriously for those who are keen.
Don't under-estimate how difficult it is to get around Oxford, and how much that might matter to your choice of school. Traffic is very bad, many routes through town are blocked to private cars, and this will get worse once the congestion charge points get replaced by bus filters. Local bus connections between residential parts of the city are poor and usually involve getting a bus into town, walking across town, and getting another bus out again. Cycling is a possibility but it depends on your risk tolerance. The schools have a private bus service, but only right after school, so if you aren't walkable or can't pick them up, then going by bus means they can't do clubs (which is a shame since both school have loads of extra curriculars). In other words, if you're choosing between Headington and Oxford High, exactly which part of town you are planning to live in might make quite a big difference (especially as you also have another child to get to school).