As far as I can tell, minimize_with_cst does what it says on the tin. It imposes harmonic constraints on all C-alpha/C-alpha distances, and then minimizes the structure.
Relax, on the other hand, does cycles of repacking and minimization with ramping repulsive values. By default, no constraints are added during relax, although they’re available as options. This is a much more aggressive optimization, and has the potential to substantially alter the conformation of the structure.
If you’ve examined the relaxed structure and are satisfied that it’s reasonably close to the experimental structure, I would imagine that it could be used instead of minimize_with_cst, as the structure would definitely be minimized. I don’t think this sort of preparation has been tested, though, so I can’t say if it would have the same correlation to experimental data as the standard minimize_with_cst/ddg_monomer approach does.
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