I would like to know whether, at least in principle, minimization of energy with respect to nuclear coordinates leads to the same result as minimization of cell energy with respect to lattice parameters. Is one way computationally more advantageous than the other? Thanks in advance, also I'm sorry if the question might not be accurately formulated.
Minimizing energy with respect to nuclear coordinates and with respect to lattice parameters are two very different things.
Minimizing energy with respect to nuclear coordinates can be used for periodic and isolated systems.
In the case of a periodic system, this will lead to knowing how the atoms and/or molecules are arranged inside a given crystallographic cell. In this instance, the crystal symmetry is a constraint on your system. If your system is an isolated molecule, there are no constraints, and you will have the conformer with the lowest energy.
Minimizing the lattice parameters (in general, together with the nuclear coordinates) is done when you are starting from a bad structure, or you need to know if the system can have another crystallographic phase. If you have crystallographic evidence that there are no other phases, then you can use the experimental lattice parameters as constants, and there is no need to optimize them.
Is one way computationally more advantageous than the other? There is no such thing as an advantage. All of this will depend on what you are studying and your needs.