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I'd assume loading both would make the curvature go to 0 as you'd be making the positive curve of the saddle flatten but only accentuating the negative curve. Can't imagine the negative curve bending to positive under loading (I know it can't but if that's our argument for saddles being stiffer...).
Alas, I'm sure it'll be covered in due course.
HHC
You're not alone! On re-engaging of my brain, loading a dome tries to flatten it i.e. movin from +ve curvature to 0 curvature. But, I think it depends how you load your structures. Good knows. Ask a (academic) structural engineer!