Boys appear to be failing behind girls in both public and private schools. It's good to hear that you are willing to sacrifice to ensure your child receives a quality education, but I caution against simply assuming that private schools don't have many of the same issues. While I'd agree, on the whole, that many private schools outclass their public equivalents, private schools often have their own set of issues.
I recommend a book that I just started reading myself, "Why Boys Fail: Saving Our Sons from an Educational System That's Leaving Them Behind", by Roger Whitmire. While I'm only two chapters in, it's already clear that he's done a lot of research in this area. Being armed with some real data behind this issue can help you choose a private school that understands how to educate both boys and girls.