Time complexity of prims algorithm when binary heap is used is $O(ElogV)$
Time complexity of prims algorithm when fibonacci heap is used is $O(E + VlogV)$
Now, for a sparse graph(where the number of edges are of the order of number of vertices i.e. $E=\theta(V)$, then time complexity becomes
$O(VlogV)$ for binary heap and
$O(V + VlogV)=O(VlogV)$ for fibonacci heap
For a dense graph (where edges might exist in every two vertices i.e. near to $\frac{V(V-1)}{2}$ which is $O(V^2)$ i.e. $E=O(V^2)$), the time complexity becomes,
$O(V^2logV)$ for binary heap and
$O(V^2+VlogV) = O(V^2)$ for fibonacci heap.