I have a 3D string vector in C++:
vector>> some_vector
That I am trying is to find a fast method to all
When you initialize a vector of vectors in the first method, a temporary vector is allocated and then copied into the outer vector the required number of times. This means you have an extra allocation that is unnecessary and the new elements are initialized by copying their value from another data structure, which uses more memory accesses.
Resizing the vectors as per the second method is more ugly but avoids the extra allocation. Furthermore the new elements are created by the default constructor and do not need to copy from other vectors. This will also be faster.
If speed matters (and maybe it doesn't, premature optimization and all that), then you must use the second method (OR a single-block allocation as suggested by the other answers). I don't have faith that a compiler can simply "optimize" away the inefficiency of the first method.