Not sure where you went to school, but for most non-ghetto Houston high schools I would disagree. The IB programs at Lamar, or Bellaire, or Westside, or Memorial, or Stratford, or Clements, or lots of other suburban high schools are every bit as good as anything you can get at Kinkaid, or St.Thomas, or Strake/St.Agnes. Most of the other Houston area private schools are sub-standard to these programs. The only exception is St. John's. SJ's stands alone at the top.
As touched on by other posters, the private schools are all better on average, but it's only because they have the ability to keep the bottom third of students off campus. I went to Lamar were 40% of my freshman class dropped out before graduating. There's no way to overcome those numbers if you only consider a school's averages.
If your goal is to shelter your kids from rubbing shoulders with poors, or indoctrinate them with religious dogma, private school is perfect. If you want them educated, HISD can do just fine.
Bernard