I can not see why MSD radix sort is theoretically as efficient as LSD radix sort
If I understand OP's question correctly - the question is what is the time-complexity estimate for MSD radix sort, taking into account what OP calls AmountofNodes or recursive frames for an MSD sort, which must fill the count[] array ($R$) per each recursive frame and than iterate through the count[] array to create subfiles. I couldn't find this in the literature and I presume jsguy hasn't found a satisfactory explanation either. 

I'm going to assume we are talking about the Naive MSD sort as described in the OP's pseudo code. (otherwise if you have 20 items in a subfile and $R = 256$, a hash-table would be significantly cheaper than the count[] array). 

From the looks of it worst case time-complexity for that should be $\Theta(NW + NR^{(W-1)})$, where each item is unique. Specifically a worst-case number of $R$ calls will happen if none of the recursive calls terminate early (before $W_{i-1}$) and if a subfile is broken up as much as possible from the root (the maximum number of recursive calls started from any subfile is $R$).

Considering a set of subfiles $N$ - if the set is already dense duplicates only cost $W$ ($N &gt; R^W$ and all combinations appear), if the set is sparse ($N &lt; R^W$ and without duplicates), adding a duplicate costs at most $R(W-1)$ (if a single subfile would otherwise have terminated early at $W_1$). 

If the set $N$ is sparse, either some combinations will not diverge at level $W_0$ (which is always more expensive than diverging at some further level $W_x$) or as many as possible will diverge at each level but some will terminate before $W_{i-1}$ because the branch will have only a single item remaining - therefore for sparse sets the worse-case is to have maximal divergence at each level $W$ until there are two duplicates in each subfile, for which the above estimate of $R(W-1)$ per item should apply. 



edit: As to why people use MSD Radix sort, I hope someone that works with an application that utilizes Radix sort can answer that, I suspect there are cases like long RNA strings where there are very long strings with a very small $R$, and the ability to parallelize is an advantage (just a guess though). My worst case estimate definitely sounds pretty bad, but I think in practice no one tries to split a file of two duplicate items into $R$ buckets at every single $W_i$.