Let $X$ be a complex projective variety (you may assume it is smooth, or has mild singularities, is simply connected or any other assumption which makes you happy)
Let $Big(X)$ and $Amp(X)$ be the cone of big and ample divisors respectively. Both are open cones in $N^1(X)$.
What can we say if we know they are equal? Note that in general $Amp(X) \subseteq Big(X)$ and the former is smaller when there are effective divisors which are not nef.