You've already summarized the differences in your question, but to be complete: ISIF=3 has an additional degree of freedom that allows the cell volume to change. In principle, there should be no difference in what the final relaxed structure will be. So another way of asking this question might be, what type of relaxations require my cell volume to be fixed?
Here are some suggestions based on my own experiences.
Situations where ISIF=3 is NOT acceptable:
- Calculations with vacuum (slabs or molecules). This is the most important one. Especially in slab calculations, allowing the cell volume to change will almost always result in your vacuum being reduced to zero (cell becomes periodic).
- Calculations where the equilibrium cell volume has already been optimized prior to relaxation. Often times bulk calculations with varying cell volumes and little to no relaxation will be performed to find the bulk lattice parameter by fit to an equation of state. There are many Equations of State, the Materials Project has a nice table summarizing some of them here.
- Calculations of materials under strain. Allowing the volume to change can result in the strain relaxing out.
Situations where I recommend ISIF=4 over ISIF=3:
- During calculations to determine a fit to an Equation of State. These should have fixed volume throughout the calculation, although each individual calculation differs in volume.
- Initial relaxation in systems where the equilibrium lattice parameter is unknown. I find that there is a significant speedup if I manually sample lattice parameters first to get close to equilibrium before allowing the volume itself to change in the simulation.
- Relaxation when the forces in your system are large (>2 eV/Å). In my experience ISIF=3 can lead to bad convergence. Relax with ISIF=4 first and then switch to ISIF=3 if you'd like.
Situations where I recommend ISIF=3 over ISIF=4:
- When you desire a very accurate total volume. I would do this after finding a relaxed structure at a lower ENCUT first.
Hopefully other members of the community can also give you more advice based on their experiences!