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Most of the flexing happens in the sidewalls, up the pressure and the sidewalls will flex less, which leads to less fatigue overall. Remember, fatigue comes from cyclic loads, not constant loads.
As far a grip is concerned, it will be different for every tire and load. You have to check your own contact patch and test your car. From what I read, generally in passenger cars radials on average paved roads underinflation<overinflation<recommended inflation. Hyperinflation would probably rate around underinflation. Note that grip ≠ handling. Sidewall stiffness plays a big role in handling ability.
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