Considering vector value shape function, degree of freedom numbering can be done in two ways:
First, iterate through all the components($u_x,u_y,u_z$) of a node then move to the next node.
$$ [u_{1x}, u_{1y}, u_{1z}, u_{2x}, u_{2y}, u_{3z}, ..., u_{nx}, u_{ny}, u_{nz}]$$
Second, iterate through the first component of each node of the element, then the second component and so on. $$ [u_{1x}, u_{2x}, ..., u_{nx}, u_{1y}, u_{2y},..., u_{ny}, u_{1z}, u_{2z}, ... u_{nz}]$$
Is there any benefit of one over another numbering scheme in terms of efficiency and implementation of FEM?
In terms of efficiency, there won't be that much gain or loss because the access to the memory remains the same. In terms of implementation, there will be some changes, like, to access the coordinates for the first vertex, you have to access the i+nDofs entry and i+2nDofs entry, whereas in the second case this will be easier. In the end, it depends on your way of coding.