Design and Analysis of algorithm – d-ary heap and fibonacci heap comparison for Dijkstra

For what asymptotic growth rates of m, with respect to n, can we choose d so that a d-heap
yields better performance, asymptotically than Fibonacci heap, or which heap data structure performs asymptotically better than other.

We can consider a scenario where d-heaps are as good as Fibonacci heaps (with less bookkeeping).