Note that reduce(vcat, fun.(array)) may well hit a special method for vectors of vectors or matrices, which allocates one array to write into. There is no such method for mapreduce(fun, vcat, array), and thus it will call vcat many times, allocating length(array)-1 arrays in the process. This will probably be much more expensive than the one temporary array from fun.(array).
If fun(a) returns a vector, then you can try vec(stack(fun, array)), with using Compat first.