For example, consider $\mathbb{F}_2[x]$. Both $(x^3+x+1)$ and $(x^3+x^2+1)$ are maximal, since both polynomials are irreducible (degree is 3, and there are no roots). Then we know the fields $\mathbb{F}_2[x] / (x^3+x+1)$ and $\mathbb{F}_2[x] / (x^3+x^2+1)$ are fields order 8, since the basis is $\{1, \theta,\theta^2\}$. But are the two fields isomorphic?
My guess is that they are not, since in $\mathbb{F}_2[x] / (x^3+x+1)$, $\theta^3=\theta+1$, whereas in $\mathbb{F}_2[x] / (x^3+x^2+1)$, $\theta^3=\theta^2+1$.