I don't find aero bars any more or less stiff than any other bar shape. It really depends on the manufacturer, just like any other bar.
If you're looking to do IAB you'll want something that is flattish on top. I ride an Aerofly and I find it very stable and comfortable doing the IAB thing. I used to use an Aeronova and the tops slope downward from the stem which makes IAB uncomfortable and squirrely, but it had a really comfy notching thing going on where the bars bend forward that makes a sphinx style position really nice and quite low. The Aeronova's reach is pretty long too so you get decent support along the whole forearm. The downside is, when you sprint you'll more than likely bump your wrists. Sphinx is obviously doable on the aeroflys as well but it cradles your forearms less when you're doing it.
So really it's just a style choice. Whichever way you prefer to get aero is the way you should go. Eastons and Zipps are pretty flat on top as well.